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Popular >

2x^2+5x-1>0

Solution

2 x^{2} + 5 x - 1 > 0

Solution

x < \frac{- 33 - 5}{4} or x > \frac{33 - 5}{4}

+2

Interval Notation

(- \infty, \frac{- 33 - 5}{4}) \cup (\frac{33 - 5}{4}, \infty)

Decimal Notation

x < - 2.68614 \dots or x > 0.18614 \dots

Solution steps

2 x^{2} + 5 x - 1 > 0

Complete the square

2 x^{2} + 5 x - 1 : 2 (x + \frac{5}{4})^{2} - \frac{33}{8}

2 (x + \frac{5}{4})^{2} - \frac{33}{8} > 0

Move

\frac{33}{8}

to the right side

2 (x + \frac{5}{4})^{2} > \frac{33}{8}

Divide both sides by

2

(x + \frac{5}{4})^{2} > \frac{33}{16}

For

u^{n} > a

, if

n

is even then

x + \frac{5}{4} < - \frac{33}{16} or x + \frac{5}{4} > \frac{33}{16}

x + \frac{5}{4} < - \frac{33}{16} : x < \frac{- 33 - 5}{4}

x + \frac{5}{4} > \frac{33}{16} : x > \frac{33 - 5}{4}

Combine the intervals

x < \frac{- 33 - 5}{4} or x > \frac{33 - 5}{4}

Popular Examples

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\frac{( x - 3 ) ( 4 - 2 x ) ( 1 - 3 x )}{( 1 - 4 x ) ( 5 - 3 x )} \leq 0

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x^{4} - 8 x^{2} - 9

14 x \geq 56

simplify ((12xy^7)/(4x^4y^3))^2 simplify

(\frac{12 x y ^{7}}{4 x ^{4} y ^{3}})^{2}

Frequently Asked Questions (FAQ)

What is 2x^2+5x-1>0 ?
The solution to 2x^2+5x-1>0 is x<(-sqrt(33)-5)/4 \lor x>(sqrt(33)-5)/4