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x^2+6=0

x^2+6=0 equation

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Numerical solution:

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The solution

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 2        
x  + 6 = 0
$$x^{2} + 6 = 0$$
Simplify
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
$$a = 1$$
$$b = 0$$
$$c = 6$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (6) = -24

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
$$x_{1} = \sqrt{6} i$$
$$x_{2} = - \sqrt{6} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 6$$
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
          ___
x1 = -I*\/ 6
$$x_{1} = - \sqrt{6} i$$ 
         ___
x2 = I*\/ 6
$$x_{2} = \sqrt{6} i$$ 
x2 = sqrt(6)*i
Sum and product of roots [src] 
sum
      ___       ___
- I*\/ 6  + I*\/ 6
$$- \sqrt{6} i + \sqrt{6} i$$ 
=
0
$$0$$ 
product
     ___     ___
-I*\/ 6 *I*\/ 6
$$- \sqrt{6} i \sqrt{6} i$$ 
=
6
$$6$$ 
6
Numerical answer [src] 
x1 = -2.44948974278318*i
x2 = 2.44948974278318*i
x2 = 2.44948974278318*i
The graph
x^2+6=0 equation
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