What is 2x-(x^2)/2 >-21/3 ?

The solution to 2x-(x^2)/2 >-21/3 is -3sqrt(2)+2<x<3sqrt(2)+2

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2x-(x^2)/2 >-21/3

2 x - \frac{x ^{2}}{2} > - \frac{21}{3}

- 32 + 2 < x < 32 + 2

Interval Notation

(- 32 + 2, 32 + 2)

Decimal Notation

- 2.24264 \dots < x < 6.24264 \dots

Solution steps

2 x - \frac{x ^{2}}{2} > - \frac{21}{3}

Rewrite in standard form

4 x - x^{2} + 14 > 0

Complete the square

4 x - x^{2} + 14 : - (x - 2)^{2} + 18

- (x - 2)^{2} + 18 > 0

Move

18

to the right side

- (x - 2)^{2} > - 18

Multiply both sides by

- 1

(x - 2)^{2} < 18

For

u^{n} < a

, if

n

is even then

- 18 < x - 2 < 18

a < u < b

then

a < u and u < b

- 18 < x - 2 and x - 2 < 18

- 18 < x - 2 : x > - 32 + 2

x - 2 < 18 : x < 32 + 2

Combine the intervals

x > - 32 + 2 and x < 32 + 2

Merge Overlapping Intervals

- 32 + 2 < x < 32 + 2

18 < - 3 b

- \frac{2}{3} - 2

(x - 1) (x + 4) < 0

x^{- 2} \cdot x

n^{4} + 11 n^{2} + 28

What is 2x-(x^2)/2 >-21/3 ?
The solution to 2x-(x^2)/2 >-21/3 is -3sqrt(2)+2<x<3sqrt(2)+2