Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+2)^4-4*(x+2)^2-5=0
- Equation x-y=2
-
Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
- Express {x} in terms of y where:
- 15*x+7*y=2
- 12*x-20*y=10
- -17*x-15*y=-17
- 6*x-2*y=20
- Derivative of:
- f*(x)
- Integral of d{x}:
- -2*x-5
- Graphing y =:
- -2*x-5
-
Identical expressions
- f*(x)=- two *x- five
- f multiply by (x) equally minus 2 multiply by x minus 5
- f multiply by (x) equally minus two multiply by x minus five
- f(x)=-2x-5
- fx=-2x-5
-
Similar expressions
- x-3x-2/53-2x-5/3
- 7x-(2x-5)=2(2x+3)
- 17-3(15-x)=(4-x)-2(x-5)
- u=f((x^2+y^2)^(1/2))
- x.diff(x)=5*x-3*y
- f*(x)=+2*x-5
- f*(x)=-2*x+5
- f*x=x^2-6*x+8
f*(x)=-2*x-5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Expand brackets in the left part
Move the summands with the unknown x
from the right part to the left part:
$$f x + 2 x = -5$$
Divide both parts of the equation by (2*x + f*x)/x
We get the answer: x = -5/(2 + f)
f*(x) = -2*x-5
Expand brackets in the left part
fx = -2*x-5
Move the summands with the unknown x
from the right part to the left part:
$$f x + 2 x = -5$$
Divide both parts of the equation by (2*x + f*x)/x
x = -5 / ((2*x + f*x)/x)
We get the answer: x = -5/(2 + f)
The solution of the parametric equation
Given the equation with a parameter:
$$f x = - 2 x - 5$$
Коэффициент при x равен
$$f + 2$$
then possible cases for f :
$$f < -2$$
$$f = -2$$
Consider all cases in more detail:
With
$$f < -2$$
the equation
$$5 - x = 0$$
its solution
$$x = 5$$
With
$$f = -2$$
the equation
$$5 = 0$$
its solution
no solutions
$$f x = - 2 x - 5$$
Коэффициент при x равен
$$f + 2$$
then possible cases for f :
$$f < -2$$
$$f = -2$$
Consider all cases in more detail:
With
$$f < -2$$
the equation
$$5 - x = 0$$
its solution
$$x = 5$$
With
$$f = -2$$
the equation
$$5 = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
5*(2 + re(f)) 5*I*im(f)
x1 = - --------------------- + ---------------------
2 2 2 2
(2 + re(f)) + im (f) (2 + re(f)) + im (f)
$$x_{1} = - \frac{5 \left(\operatorname{re}{\left(f\right)} + 2\right)}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{5 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
x1 = -5*(re(f) + 2)/((re(f) + 2)^2 + im(f)^2) + 5*i*im(f)/((re(f) + 2)^2 + im(f)^2)
Sum and product of roots
[src]
sum
5*(2 + re(f)) 5*I*im(f)
- --------------------- + ---------------------
2 2 2 2
(2 + re(f)) + im (f) (2 + re(f)) + im (f)
$$- \frac{5 \left(\operatorname{re}{\left(f\right)} + 2\right)}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{5 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
5*(2 + re(f)) 5*I*im(f)
- --------------------- + ---------------------
2 2 2 2
(2 + re(f)) + im (f) (2 + re(f)) + im (f)
$$- \frac{5 \left(\operatorname{re}{\left(f\right)} + 2\right)}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{5 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
product
5*(2 + re(f)) 5*I*im(f)
- --------------------- + ---------------------
2 2 2 2
(2 + re(f)) + im (f) (2 + re(f)) + im (f)
$$- \frac{5 \left(\operatorname{re}{\left(f\right)} + 2\right)}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} + \frac{5 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
5*(-2 - re(f) + I*im(f))
------------------------
2 2
(2 + re(f)) + im (f)
$$\frac{5 \left(- \operatorname{re}{\left(f\right)} + i \operatorname{im}{\left(f\right)} - 2\right)}{\left(\operatorname{re}{\left(f\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
5*(-2 - re(f) + i*im(f))/((2 + re(f))^2 + im(f)^2)