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2x^2+8=0

2x^2+8=0 equation

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Numerical solution:

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The solution

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2*x  + 8 = 0
$$2 x^{2} + 8 = 0$$
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
$$a = 2$$
$$b = 0$$
$$c = 8$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (2) * (8) = -64

Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)

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

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