\[{x}^{2}+2x-2=0\]

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Quadratic Formula

Complete the Square

Use the Quadratic Formula.

In general, given

a{x}^{2}+bx+c=0

, there exists two solutions where:

x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}

In this case,

a=1

b=2

and

c=-2

{x}^{}=\frac{-2+\sqrt{{2}^{2}-4\times -2}}{2},\frac{-2-\sqrt{{2}^{2}-4\times -2}}{2}

Simplify.

x=\frac{-2+2\sqrt{3}}{2},\frac{-2-2\sqrt{3}}{2}

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x=\frac{-2+2\sqrt{3}}{2},\frac{-2-2\sqrt{3}}{2}

Simplify solutions.

x=-1+\sqrt{3},-1-\sqrt{3}

Done

Decimal Form: 0.732051, -2.732051

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