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Similar expressions
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(-8x^2-4x+2)^2=0 equation
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The solution
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[src]
2 / 2 \ \- 8*x - 4*x + 2/ = 0
$$\left(\left(- 8 x^{2} - 4 x\right) + 2\right)^{2} = 0$$
Detail solution
$$\left(\left(- 8 x^{2} - 4 x\right) + 2\right)^{2} = 0$$
transform
$$- 8 x^{2} - 4 x + 2 = 0$$
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
$$a = -8$$
$$b = -4$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{\sqrt{5}}{4} - \frac{1}{4}$$
$$x_{2} = - \frac{1}{4} + \frac{\sqrt{5}}{4}$$
transform
$$- 8 x^{2} - 4 x + 2 = 0$$
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
$$a = -8$$
$$b = -4$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (-8) * (2) = 80
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{\sqrt{5}}{4} - \frac{1}{4}$$
$$x_{2} = - \frac{1}{4} + \frac{\sqrt{5}}{4}$$
Rapid solution
[src]
___
1 \/ 5
x1 = - - + -----
4 4
$$x_{1} = - \frac{1}{4} + \frac{\sqrt{5}}{4}$$
___
1 \/ 5
x2 = - - - -----
4 4
$$x_{2} = - \frac{\sqrt{5}}{4} - \frac{1}{4}$$
x2 = -sqrt(5)/4 - 1/4
Sum and product of roots
[src]
sum
___ ___ 1 \/ 5 1 \/ 5 - - + ----- + - - - ----- 4 4 4 4
$$\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) + \left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right)$$
=
-1/2
$$- \frac{1}{2}$$
product
/ ___\ / ___\ | 1 \/ 5 | | 1 \/ 5 | |- - + -----|*|- - - -----| \ 4 4 / \ 4 4 /
$$\left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right) \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)$$
=
-1/4
$$- \frac{1}{4}$$
-1/4