\[{x}^{2}+6x+4=0\]

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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=6

and

c=4

{x}^{}=\frac{-6+\sqrt{{6}^{2}-4\times 4}}{2},\frac{-6-\sqrt{{6}^{2}-4\times 4}}{2}

Simplify.

x=\frac{-6+2\sqrt{5}}{2},\frac{-6-2\sqrt{5}}{2}

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x=\frac{-6+2\sqrt{5}}{2},\frac{-6-2\sqrt{5}}{2}

Simplify solutions.

x=-3+\sqrt{5},-3-\sqrt{5}

Done

Decimal Form: -0.763932, -5.236068

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