Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=12
-
Equation 3^x=81
-
Equation x^2-8x+12=0
-
Equation x^6=-(12-8x)^3
- Express {x} in terms of y where:
- -5*x-6*y=-1
- 1*x+6*y=-6
- -5*x+6*y=-8
- -2*x-9*y=10
-
Identical expressions
- - eight *(x- eight)*(x- twenty)= zero
- minus 8 multiply by (x minus 8) multiply by (x minus 20) equally 0
- minus eight multiply by (x minus eight) multiply by (x minus twenty) equally zero
- -8(x-8)(x-20)=0
- -8x-8x-20=0
- -8*(x-8)*(x-20)=O
-
Similar expressions
- -8*(x-8)*(x+20)=0
- 8*(x-8)*(x-20)=0
- -8*(x+8)*(x-20)=0
-8*(x-8)*(x-20)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
-8*(x - 8)*(x - 20) = 0
$$\left(x - 20\right) \left(- 8 \left(x - 8\right)\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(x - 20\right) \left(- 8 \left(x - 8\right)\right) = 0$$
We get the quadratic equation
$$- 8 x^{2} + 224 x - 1280 = 0$$
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
$$a = -8$$
$$b = 224$$
$$c = -1280$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 8$$
$$x_{2} = 20$$
$$\left(x - 20\right) \left(- 8 \left(x - 8\right)\right) = 0$$
We get the quadratic equation
$$- 8 x^{2} + 224 x - 1280 = 0$$
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
$$a = -8$$
$$b = 224$$
$$c = -1280$$
, then
D = b^2 - 4 * a * c =
(224)^2 - 4 * (-8) * (-1280) = 9216
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 8$$
$$x_{2} = 20$$
Sum and product of roots
[src]
sum
8 + 20
$$8 + 20$$
=
28
$$28$$
product
8*20
$$8 \cdot 20$$
=
160
$$160$$
160