What is -2x^2+8x-1>0 ?

The solution to -2x^2+8x-1>0 is -sqrt(7/2)+2<x<sqrt(7/2)+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-2x^2+8x-1>0

- 2 x^{2} + 8 x - 1 > 0

- \frac{7}{2} + 2 < x < \frac{7}{2} + 2

Interval Notation

(- \frac{7}{2} + 2, \frac{7}{2} + 2)

Decimal Notation

0.12917 \dots < x < 3.87082 \dots

Solution steps

- 2 x^{2} + 8 x - 1 > 0

Complete the square

- 2 x^{2} + 8 x - 1 : - 2 (x - 2)^{2} + 7

- 2 (x - 2)^{2} + 7 > 0

Move

7

to the right side

- 2 (x - 2)^{2} > - 7

Multiply both sides by

- 1

2 (x - 2)^{2} < 7

Divide both sides by

2

(x - 2)^{2} < \frac{7}{2}

For

u^{n} < a

, if

n

is even then

- \frac{7}{2} < x - 2 < \frac{7}{2}

a < u < b

then

a < u and u < b

- \frac{7}{2} < x - 2 and x - 2 < \frac{7}{2}

- \frac{7}{2} < x - 2 : x > - \frac{7}{2} + 2

x - 2 < \frac{7}{2} : x < \frac{7}{2} + 2

Combine the intervals

x > - \frac{7}{2} + 2 and x < \frac{7}{2} + 2

Merge Overlapping Intervals

- \frac{7}{2} + 2 < x < \frac{7}{2} + 2

\frac{22}{4}

0.5625 x^{2} - 0.75 x + 1 = 0

x^{2} - 4 x + 5 > 0

\frac{3 π}{6}

10 x + 60 = 0

What is -2x^2+8x-1>0 ?
The solution to -2x^2+8x-1>0 is -sqrt(7/2)+2<x<sqrt(7/2)+2