Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 6*x^2+x-7=0
-
Equation (x^2-9)^2+(x^2+x-6)^2=0
-
Equation 15*x^2-4*x-3=0
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Equation (x-5)=(x+10)^2
- Express {x} in terms of y where:
- 2*x+20*y=16
- -15*x-12*y=17
- -20*x+5*y=-11
- 2*x+10*y=-5
- Integral of d{x}:
-
(x-5)
- Graphing y =:
- (x-5)
-
Identical expressions
- (x- five)=(x+ ten)^ two
- (x minus 5) equally (x plus 10) squared
- (x minus five) equally (x plus ten) to the power of two
- (x-5)=(x+10)2
- x-5=x+102
- (x-5)=(x+10)²
- (x-5)=(x+10) to the power of 2
- x-5=x+10^2
-
Similar expressions
- 2^x-5*2^x-4=11
- (x-5)=(x-10)^2
- x^2-x-5=0
- x^2-14*x-5=0
- (x+5)=(x+10)^2
(x-5)=(x+10)^2 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
$$x - 5 = \left(x + 10\right)^{2}$$
to
$$\left(x - 5\right) - \left(x + 10\right)^{2} = 0$$
Expand the expression in the equation
$$\left(x - 5\right) - \left(x + 10\right)^{2} = 0$$
We get the quadratic equation
$$- x^{2} - 19 x - 105 = 0$$
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
$$a = -1$$
$$b = -19$$
$$c = -105$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = - \frac{19}{2} - \frac{\sqrt{59} i}{2}$$
$$x_{2} = - \frac{19}{2} + \frac{\sqrt{59} i}{2}$$
left part with negative sign.
The equation is transformed from
$$x - 5 = \left(x + 10\right)^{2}$$
to
$$\left(x - 5\right) - \left(x + 10\right)^{2} = 0$$
Expand the expression in the equation
$$\left(x - 5\right) - \left(x + 10\right)^{2} = 0$$
We get the quadratic equation
$$- x^{2} - 19 x - 105 = 0$$
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
$$a = -1$$
$$b = -19$$
$$c = -105$$
, then
D = b^2 - 4 * a * c =
(-19)^2 - 4 * (-1) * (-105) = -59
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{19}{2} - \frac{\sqrt{59} i}{2}$$
$$x_{2} = - \frac{19}{2} + \frac{\sqrt{59} i}{2}$$
Sum and product of roots
[src]
sum
____ ____ 19 I*\/ 59 19 I*\/ 59 - -- - -------- + - -- + -------- 2 2 2 2
$$\left(- \frac{19}{2} - \frac{\sqrt{59} i}{2}\right) + \left(- \frac{19}{2} + \frac{\sqrt{59} i}{2}\right)$$
=
-19
$$-19$$
product
/ ____\ / ____\ | 19 I*\/ 59 | | 19 I*\/ 59 | |- -- - --------|*|- -- + --------| \ 2 2 / \ 2 2 /
$$\left(- \frac{19}{2} - \frac{\sqrt{59} i}{2}\right) \left(- \frac{19}{2} + \frac{\sqrt{59} i}{2}\right)$$
=
105
$$105$$
105
Rapid solution
[src]
____
19 I*\/ 59
x1 = - -- - --------
2 2
$$x_{1} = - \frac{19}{2} - \frac{\sqrt{59} i}{2}$$
____
19 I*\/ 59
x2 = - -- + --------
2 2
$$x_{2} = - \frac{19}{2} + \frac{\sqrt{59} i}{2}$$
x2 = -19/2 + sqrt(59)*i/2
Numerical answer
[src]
x1 = -9.5 + 3.8405728739343*i
x2 = -9.5 - 3.8405728739343*i
x2 = -9.5 - 3.8405728739343*i
The graph