What is (-10)/(2+sqrt(14)) ?

The solution to (-10)/(2+sqrt(14)) is 2-sqrt(14)

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simplify (-10)/(2+sqrt(14))

simplify

\frac{- 10}{2 + 14}

2 - 14

Decimal Notation

- 1.74165 \dots

Solution steps

\frac{- 10}{2 + 14}

Multiply by the conjugate

\frac{2 - 14}{2 - 14}

= \frac{- 10 ( 2 - 14 )}{( 2 + 14 ) ( 2 - 14 )}

Expand

- 10 (2 - 14) : - 20 + 1014

Expand

(2 + 14) (2 - 14) : - 10

= \frac{- 20 + 10 14}{- 10}

Factor out common term

10 : 10 (- 2 + 14)

= \frac{10 ( - 2 + 14 )}{- 10}

Cancel the common factor:

10

= \frac{- 2 + 14}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (- 2 + 14)

- (- 2 + 14) = 2 - 14

= 2 - 14

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