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Popular >

-2x^2-2x-1<0

Solution

- 2 x^{2} - 2 x - 1 < 0

Solution

True for all x

+1

Interval Notation

(- \infty, \infty)

Solution steps

- 2 x^{2} - 2 x - 1 < 0

Complete the square

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

- 2 (x + \frac{1}{2})^{2} - \frac{1}{2} < 0

Move

\frac{1}{2}

to the right side

- 2 (x + \frac{1}{2})^{2} < \frac{1}{2}

Multiply both sides by

- 1

2 (x + \frac{1}{2})^{2} > - \frac{1}{2}

Divide both sides by

2

(x + \frac{1}{2})^{2} > - \frac{1}{4}

If n is even,

u^{n} \geq 0

for all

u

True for all x

Popular Examples

((4x+3))/((2x-5))<6

\frac{( 4 x + 3 )}{( 2 x - 5 )} < 6

((x-4))/((2x-3))<3

\frac{( x - 4 )}{( 2 x - 3 )} < 3

x + 1 < \frac{6}{x}

4 x - x^{2} + 8 \geq 0

\frac{x - 3}{2 x - 4} > 0

Frequently Asked Questions (FAQ)

What is -2x^2-2x-1<0 ?
The solution to -2x^2-2x-1<0 is True for all x