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Popular >

x^2+x-9>= 0

Solution

x^{2} + x - 9 \geq 0

Solution

x \leq \frac{- 37 - 1}{2} or x \geq \frac{37 - 1}{2}

+2

Interval Notation

(- \infty, \frac{- 37 - 1}{2}] \cup [\frac{37 - 1}{2}, \infty)

Decimal Notation

x \leq - 3.54138 \dots or x \geq 2.54138 \dots

Solution steps

x^{2} + x - 9 \geq 0

Complete the square

x^{2} + x - 9 : (x + \frac{1}{2})^{2} - \frac{37}{4}

(x + \frac{1}{2})^{2} - \frac{37}{4} \geq 0

Move

\frac{37}{4}

to the right side

(x + \frac{1}{2})^{2} \geq \frac{37}{4}

For

u^{n} \geq a

, if

n

is even then

x + \frac{1}{2} \leq - \frac{37}{4} or x + \frac{1}{2} \geq \frac{37}{4}

x + \frac{1}{2} \leq - \frac{37}{4} : x \leq \frac{- 37 - 1}{2}

x + \frac{1}{2} \geq \frac{37}{4} : x \geq \frac{37 - 1}{2}

Combine the intervals

x \leq \frac{- 37 - 1}{2} or x \geq \frac{37 - 1}{2}

Popular Examples

factor 9xy+wx+9yz+wz factor

9 x y + w x + 9 yz + w z

25 x^{2} + 1 = 0

\frac{x - 5}{3} < \frac{22}{5}

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\frac{3}{\frac{2}{3}}

2 x^{2} - 200 = 0

Frequently Asked Questions (FAQ)

What is x^2+x-9>= 0 ?
The solution to x^2+x-9>= 0 is x<= (-sqrt(37)-1)/2 \lor x>= (sqrt(37)-1)/2