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Popular >

4x^2+x-2>0

Solution

4 x^{2} + x - 2 > 0

Solution

x < \frac{- 33 - 1}{8} or x > \frac{33 - 1}{8}

+2

Interval Notation

(- \infty, \frac{- 33 - 1}{8}) \cup (\frac{33 - 1}{8}, \infty)

Decimal Notation

x < - 0.84307 \dots or x > 0.59307 \dots

Solution steps

4 x^{2} + x - 2 > 0

Complete the square

4 x^{2} + x - 2 : 4 (x + \frac{1}{8})^{2} - \frac{33}{16}

4 (x + \frac{1}{8})^{2} - \frac{33}{16} > 0

Move

\frac{33}{16}

to the right side

4 (x + \frac{1}{8})^{2} > \frac{33}{16}

Divide both sides by

4

(x + \frac{1}{8})^{2} > \frac{33}{64}

For

u^{n} > a

, if

n

is even then

x + \frac{1}{8} < - \frac{33}{64} or x + \frac{1}{8} > \frac{33}{64}

x + \frac{1}{8} < - \frac{33}{64} : x < \frac{- 33 - 1}{8}

x + \frac{1}{8} > \frac{33}{64} : x > \frac{33 - 1}{8}

Combine the intervals

x < \frac{- 33 - 1}{8} or x > \frac{33 - 1}{8}

Popular Examples

-4(-0.8n+5.3)<= 4.4n-8(1-1.1n)

- 4 (- 0.8 n + 5.3) \leq 4.4 n - 8 (1 - 1.1 n)

factor p^2-6-q*(p^2-6)^2 factor

p^{2} - 6 - q \cdot (p^{2} - 6)^{2}

2 x \cdot (1 - x) = x - 6

6 x + 10 > 5 x - 12

6 x^{2} - 6 x - 36 = 0

Frequently Asked Questions (FAQ)

What is 4x^2+x-2>0 ?
The solution to 4x^2+x-2>0 is x<(-sqrt(33)-1)/8 \lor x>(sqrt(33)-1)/8