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Popular >

x^2+3x+1>0

Solution

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

Solution

x < \frac{- 5 - 3}{2} or x > \frac{5 - 3}{2}

+2

Interval Notation

(- \infty, \frac{- 5 - 3}{2}) \cup (\frac{5 - 3}{2}, \infty)

Decimal Notation

x < - 2.61803 \dots or x > - 0.38196 \dots

Solution steps

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

Complete the square

x^{2} + 3 x + 1 : (x + \frac{3}{2})^{2} - \frac{5}{4}

(x + \frac{3}{2})^{2} - \frac{5}{4} > 0

Move

\frac{5}{4}

to the right side

(x + \frac{3}{2})^{2} > \frac{5}{4}

For

u^{n} > a

, if

n

is even then

x + \frac{3}{2} < - \frac{5}{4} or x + \frac{3}{2} > \frac{5}{4}

x + \frac{3}{2} < - \frac{5}{4} : x < \frac{- 5 - 3}{2}

x + \frac{3}{2} > \frac{5}{4} : x > \frac{5 - 3}{2}

Combine the intervals

x < \frac{- 5 - 3}{2} or x > \frac{5 - 3}{2}

Popular Examples

factor x^3-3x^2+4x-12 factor

x^{3} - 3 x^{2} + 4 x - 12

\frac{7 x}{8} = 14

simplify sqrt(2)^2 simplify

2^{2}

- 1.6 < m - 2.5

simplify \sqrt[4]{147}simplify

Frequently Asked Questions (FAQ)

What is x^2+3x+1>0 ?
The solution to x^2+3x+1>0 is x<(-sqrt(5)-3)/2 \lor x>(sqrt(5)-3)/2