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x^2=-3

x^2=-3 equation

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Numerical solution:

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The solution

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 2     
x  = -3
$$x^{2} = -3$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$x^{2} = -3$$
to
$$x^{2} + 3 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 3$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (3) = -12

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
$$x_{1} = \sqrt{3} i$$
$$x_{2} = - \sqrt{3} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 3$$
The graph
Rapid solution [src]
          ___
x1 = -I*\/ 3 
$$x_{1} = - \sqrt{3} i$$
         ___
x2 = I*\/ 3 
$$x_{2} = \sqrt{3} i$$
x2 = sqrt(3)*i
Sum and product of roots [src]
sum
      ___       ___
- I*\/ 3  + I*\/ 3 
$$- \sqrt{3} i + \sqrt{3} i$$
=
0
$$0$$
product
     ___     ___
-I*\/ 3 *I*\/ 3 
$$- \sqrt{3} i \sqrt{3} i$$
=
3
$$3$$
3
Numerical answer [src]
x1 = 1.73205080756888*i
x2 = -1.73205080756888*i
x2 = -1.73205080756888*i
The graph
x^2=-3 equation