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x^2+8x+12=0

x^2+8x+12=0 equation

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Numerical solution:

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The solution

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 2               
x  + 8*x + 12 = 0
$$\left(x^{2} + 8 x\right) + 12 = 0$$
Detail solution
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
$$a = 1$$
$$b = 8$$
$$c = 12$$
, then
D = b^2 - 4 * a * c = 

(8)^2 - 4 * (1) * (12) = 16

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

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

or
$$x_{1} = -2$$
$$x_{2} = -6$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 8$$
$$q = \frac{c}{a}$$
$$q = 12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = 12$$
The graph
Rapid solution [src]
x1 = -6
$$x_{1} = -6$$
x2 = -2
$$x_{2} = -2$$
x2 = -2
Sum and product of roots [src]
sum
-6 - 2
$$-6 - 2$$
=
-8
$$-8$$
product
-6*(-2)
$$- -12$$
=
12
$$12$$
12
Numerical answer [src]
x1 = -2.0
x2 = -6.0
x2 = -6.0
The graph
x^2+8x+12=0 equation