Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x/4+x=4
-
Equation x^2+11=0
- Equation x+y=5
-
Equation 1*(x-1)*(x-3)=0
- Express {x} in terms of y where:
- -11*x-3*y=14
- -1*x-17*y=-12
- 20*x+18*y=-9
- -2*x+20*y=-2
- Limit of the function:
- f*x
- Derivative of:
- f*x
- Integral of d{x}:
- x^2-6*x+8
- Graphing y =:
- x^2-6*x+8
- Factor polynomial:
- x^2-6*x+8
-
Identical expressions
- f*x=x^ two - six *x+ eight
- f multiply by x equally x squared minus 6 multiply by x plus 8
- f multiply by x equally x to the power of two minus six multiply by x plus eight
- f*x=x2-6*x+8
- f*x=x²-6*x+8
- f*x=x to the power of 2-6*x+8
- fx=x^2-6x+8
- fx=x2-6x+8
-
Similar expressions
- f*(x)=1/3*x^3+a
- f*x=x^2+6*x+8
- f*x=x^2-6*x-8
- x2*y(x2).diff(x2).diff(x2)=(y(x2).diff(x2))*2
f*x=x^2-6*x+8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$f x = \left(x^{2} - 6 x\right) + 8$$
to
$$f x + \left(\left(- x^{2} + 6 x\right) - 8\right) = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -1$$
$$b = f + 6$$
$$c = -8$$
, then
The equation has two roots.
or
$$x_{1} = \frac{f}{2} - \frac{\sqrt{\left(f + 6\right)^{2} - 32}}{2} + 3$$
$$x_{2} = \frac{f}{2} + \frac{\sqrt{\left(f + 6\right)^{2} - 32}}{2} + 3$$
left part with negative sign.
The equation is transformed from
$$f x = \left(x^{2} - 6 x\right) + 8$$
to
$$f x + \left(\left(- x^{2} + 6 x\right) - 8\right) = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -1$$
$$b = f + 6$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(6 + f)^2 - 4 * (-1) * (-8) = -32 + (6 + f)^2
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{f}{2} - \frac{\sqrt{\left(f + 6\right)^{2} - 32}}{2} + 3$$
$$x_{2} = \frac{f}{2} + \frac{\sqrt{\left(f + 6\right)^{2} - 32}}{2} + 3$$
Vieta's Theorem
rewrite the equation
$$f x = \left(x^{2} - 6 x\right) + 8$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- f x + x^{2} - 6 x + 8 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - f - 6$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = f + 6$$
$$x_{1} x_{2} = 8$$
$$f x = \left(x^{2} - 6 x\right) + 8$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- f x + x^{2} - 6 x + 8 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - f - 6$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = f + 6$$
$$x_{1} x_{2} = 8$$
The graph
Sum and product of roots
[src]
sum
/ _________________________________________________________________ \ _________________________________________________________________ / _________________________________________________________________ \ _________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/| | 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|
| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------|| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *cos|---------------------------------------------------------------| | \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------|| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *cos|---------------------------------------------------------------|
re(f) |im(f) \ 2 /| \ 2 / re(f) |im(f) \ 2 /| \ 2 /
3 + ----- + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------ + 3 + ----- + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------
2 \ 2 2 / 2 2 \ 2 2 / 2
$$\left(i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(f\right)}}{2} + 3\right) + \left(i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(f\right)}}{2} + 3\right)$$
=
/ _________________________________________________________________ \ / _________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| | 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/||
| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------|| | \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------||
|im(f) \ 2 /| |im(f) \ 2 /|
6 + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------| + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------| + re(f)
\ 2 2 / \ 2 2 /
$$i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) + i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) + \operatorname{re}{\left(f\right)} + 6$$
product
/ / _________________________________________________________________ \ _________________________________________________________________ \ / / _________________________________________________________________ \ _________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| | | \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------|| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *cos|---------------------------------------------------------------|| | | \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------|| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *cos|---------------------------------------------------------------|| | re(f) |im(f) \ 2 /| \ 2 /| | re(f) |im(f) \ 2 /| \ 2 /| |3 + ----- + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------|*|3 + ----- + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------| \ 2 \ 2 2 / 2 / \ 2 \ 2 2 / 2 /
$$\left(i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(f\right)}}{2} + 3\right) \left(i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(f\right)}}{2} + 3\right)$$
=
8
$$8$$
8
Rapid solution
[src]
/ _________________________________________________________________ \ _________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|
| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------|| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *cos|---------------------------------------------------------------|
re(f) |im(f) \ 2 /| \ 2 /
x1 = 3 + ----- + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------
2 \ 2 2 / 2
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(f\right)}}{2} + 3$$
/ _________________________________________________________________ \ _________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|| 4 / 2 / 2 2 \ |atan2\12*im(f) + 2*im(f)*re(f), 4 + re (f) - im (f) + 12*re(f)/|
| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *sin|---------------------------------------------------------------|| \/ (12*im(f) + 2*im(f)*re(f)) + \4 + re (f) - im (f) + 12*re(f)/ *cos|---------------------------------------------------------------|
re(f) |im(f) \ 2 /| \ 2 /
x2 = 3 + ----- + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------
2 \ 2 2 / 2
$$x_{2} = i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{im}{\left(f\right)}}{2}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 12 \operatorname{im}{\left(f\right)},\left(\operatorname{re}{\left(f\right)}\right)^{2} + 12 \operatorname{re}{\left(f\right)} - \left(\operatorname{im}{\left(f\right)}\right)^{2} + 4 \right)}}{2} \right)}}{2} + \frac{\operatorname{re}{\left(f\right)}}{2} + 3$$
x2 = i*(((2*re(f)*im(f) + 12*im(f))^2 + (re(f)^2 + 12*re(f) - im(f)^2 + 4)^2)^(1/4)*sin(atan2(2*re(f)*im(f) + 12*im(f, re(f)^2 + 12*re(f) - im(f)^2 + 4)/2)/2 + im(f)/2) + ((2*re(f)*im(f) + 12*im(f))^2 + (re(f)^2 + 12*re(f) - im(f)^2 + 4)^2)^(1/4)*cos(atan2(2*re(f)*im(f) + 12*im(f), re(f)^2 + 12*re(f) - im(f)^2 + 4)/2)/2 + re(f)/2 + 3)