\[2{x}^{2}-x-1=0\]

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Examples

Split the second term in

2{x}^{2}-x-1

into two terms.

Multiply the coefficient of the first term by the constant term.

2\times -1=-2

Ask: Which two numbers add up to

-1

and multiply to

-2

1

and

-2

Split

-x

as the sum of

x

and

-2x

2{x}^{2}+x-2x-1

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

Factor out common terms in the first two terms, then in the last two terms.

x(2x+1)-(2x+1)=0

Factor out the common term

2x+1

(2x+1)(x-1)=0

Solve for

x

Ask: When will

(2x+1)(x-1)

equal zero?

When

2x+1=0

x-1=0

Solve each of the 2 equations above.

x=-\frac{1}{2},1

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x=-\frac{1}{2},1

Done

Decimal Form: -0.5, 1

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