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Popular >

x^2-3x-1>0

Solution

x^{2} - 3 x - 1 > 0

Solution

x < \frac{- 13 + 3}{2} or x > \frac{13 + 3}{2}

+2

Interval Notation

(- \infty, \frac{- 13 + 3}{2}) \cup (\frac{13 + 3}{2}, \infty)

Decimal Notation

x < - 0.30277 \dots or x > 3.30277 \dots

Solution steps

x^{2} - 3 x - 1 > 0

Complete the square

x^{2} - 3 x - 1 : (x - \frac{3}{2})^{2} - \frac{13}{4}

(x - \frac{3}{2})^{2} - \frac{13}{4} > 0

Move

\frac{13}{4}

to the right side

(x - \frac{3}{2})^{2} > \frac{13}{4}

For

u^{n} > a

, if

n

is even then

x - \frac{3}{2} < - \frac{13}{4} or x - \frac{3}{2} > \frac{13}{4}

x - \frac{3}{2} < - \frac{13}{4} : x < \frac{- 13 + 3}{2}

x - \frac{3}{2} > \frac{13}{4} : x > \frac{13 + 3}{2}

Combine the intervals

x < \frac{- 13 + 3}{2} or x > \frac{13 + 3}{2}

Popular Examples

3 (8 - x) = 15

simplify (-4)^{-5}simplify

(- 4)^{- 5}

u^{2} - 5 u + 4 = 0

factor 15x^4-17x^2-4 factor

15 x^{4} - 17 x^{2} - 4

simplify sqrt(484)simplify

484

Frequently Asked Questions (FAQ)

What is x^2-3x-1>0 ?
The solution to x^2-3x-1>0 is x<(-sqrt(13)+3)/2 \lor x>(sqrt(13)+3)/2