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x^2=2x+8

x^2=2x+8 equation

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Numerical solution:

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The solution

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 2          
x  = 2*x + 8
$$x^{2} = 2 x + 8$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$x^{2} = 2 x + 8$$
to
$$x^{2} + \left(- 2 x - 8\right) = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -8$$
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (1) * (-8) = 36

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 4$$
$$x_{2} = -2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -8$$
The graph
Rapid solution [src]
x1 = -2
$$x_{1} = -2$$
x2 = 4
$$x_{2} = 4$$
x2 = 4
Sum and product of roots [src]
sum
-2 + 4
$$-2 + 4$$
=
2
$$2$$
product
-2*4
$$- 8$$
=
-8
$$-8$$
-8
Numerical answer [src]
x1 = 4.0
x2 = -2.0
x2 = -2.0
The graph
x^2=2x+8 equation