$2{x}^{2}-2x-1=0$

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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=2

b=-2

and

c=-1

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

Simplify.

x=\frac{2+2\sqrt{3}}{4},\frac{2-2\sqrt{3}}{4}

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x=\frac{2+2\sqrt{3}}{4},\frac{2-2\sqrt{3}}{4}

Simplify solutions.

x=\frac{1+\sqrt{3}}{2},\frac{1-\sqrt{3}}{2}

Done

Decimal Form: 1.366025, -0.366025

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2x2−2x−1=02{x}^{2}-2x-1=02x2−2x−1=0