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Popular >

x^2+x-1>= 0

Solution

x^{2} + x - 1 \geq 0

Solution

x \leq \frac{- 5 - 1}{2} or x \geq \frac{5 - 1}{2}

+2

Interval Notation

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

Decimal Notation

x \leq - 1.61803 \dots or x \geq 0.61803 \dots

Solution steps

x^{2} + x - 1 \geq 0

Complete the square

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

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

Move

\frac{5}{4}

to the right side

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

For

u^{n} \geq a

, if

n

is even then

x + \frac{1}{2} \leq - \frac{5}{4} or x + \frac{1}{2} \geq \frac{5}{4}

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

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

Combine the intervals

x \leq \frac{- 5 - 1}{2} or x \geq \frac{5 - 1}{2}

Popular Examples

9 + n < 10

-3x^2+3=(x+1)(x-1)

- 3 x^{2} + 3 = (x + 1) (x - 1)

- 27 = 9 (- 1 + x)

factor 64x^3-343 factor

64 x^{3} - 343

simplify sqrt(3^2+3^2)simplify

3^{2} + 3^{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