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x^2=-2

x^2=-2 equation

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Numerical solution:

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The solution

You have entered [src] 
 2     
x  = -2
x2=−2x^{2} = -2
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
x2=−2x^{2} = -2
to
x2+2=0x^{2} + 2 = 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=0b = 0
c=2c = 2
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (2) = -8

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
x1=2ix_{1} = \sqrt{2} i
Simplify
x2=−2ix_{2} = - \sqrt{2} i
Simplify
Vieta's Theorem
it is reduced quadratic equation
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=2q = 2
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=2x_{1} x_{2} = 2
The graph
02468-10-8-6-4-210-50100
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
        ___       ___
0 - I*\/ 2  + I*\/ 2
(0−2i)+2i\left(0 - \sqrt{2} i\right) + \sqrt{2} i 
=
0
00 
product
       ___     ___
1*-I*\/ 2 *I*\/ 2
2i1(−2i)\sqrt{2} i 1 \left(- \sqrt{2} i\right) 
=
2
22 
2
Rapid solution [src] 
          ___
x1 = -I*\/ 2
x1=−2ix_{1} = - \sqrt{2} i
Simplify 
         ___
x2 = I*\/ 2
x2=2ix_{2} = \sqrt{2} i
Simplify
Numerical answer [src] 
x1 = -1.4142135623731*i
x2 = 1.4142135623731*i
x2 = 1.4142135623731*i
The graph
x^2=-2 equation
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