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Popular >

x^2+x-1>0

Solution

x^{2} + x - 1 > 0

Solution

x < \frac{- 5 - 1}{2} or x > \frac{5 - 1}{2}

+2

Interval Notation

(- \infty, \frac{- 5 - 1}{2}) \cup (\frac{5 - 1}{2}, \infty)

Decimal Notation

x < - 1.61803 \dots or x > 0.61803 \dots

Solution steps

x^{2} + x - 1 > 0

Complete the square

x^{2} + x - 1 : (x + \frac{1}{2})^{2} - \frac{5}{4}

(x + \frac{1}{2})^{2} - \frac{5}{4} > 0

Move

\frac{5}{4}

to the right side

(x + \frac{1}{2})^{2} > \frac{5}{4}

For

u^{n} > a

, if

n

is even then

x + \frac{1}{2} < - \frac{5}{4} or x + \frac{1}{2} > \frac{5}{4}

x + \frac{1}{2} < - \frac{5}{4} : x < \frac{- 5 - 1}{2}

x + \frac{1}{2} > \frac{5}{4} : x > \frac{5 - 1}{2}

Combine the intervals

x < \frac{- 5 - 1}{2} or x > \frac{5 - 1}{2}

Popular Examples

simplify-9xy^2(-11x^5y^5)simplify

- 9 x y^{2} (- 11 x^{5} y^{5})

- 9 - 3 x \leq 0

- 4 \leq - 2 x + 4 < 8

simplify-1/2+1/2 simplify

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

simplify (1/x+1/y)^2 simplify

(\frac{1}{x} + \frac{1}{y})^{2}

Frequently Asked Questions (FAQ)

What is x^2+x-1>0 ?
The solution to x^2+x-1>0 is x<(-sqrt(5)-1)/2 \lor x>(sqrt(5)-1)/2