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Similar expressions
- 8*(x-8)*(x-20)=0
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-8*(x-8)*(x-20)=0 equation
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The solution
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[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