What is (500000)/(x^2+400)<260 ?

The solution to (500000)/(x^2+400) (30sqrt(22))/(sqrt(13))

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(500000)/(x^2+400)<260

\frac{500000}{x ^{2} + 400} < 260

x < - \frac{30 22}{13} or x > \frac{30 22}{13}

Interval Notation

(- \infty, - \frac{30 22}{13}) \cup (\frac{30 22}{13}, \infty)

Decimal Notation

x < - 39.02661 \dots or x > 39.02661 \dots

Solution steps

\frac{500000}{x ^{2} + 400} < 260

Rewrite in standard form

\frac{- 260 x ^{2} + 396000}{x ^{2} + 400} < 0

Factor

\frac{- 260 x ^{2} + 396000}{x ^{2} + 400} : \frac{- 20 ( 13 x + 30 22 ) ( 13 x - 30 22 )}{x ^{2} + 400}

\frac{- 20 ( 13 x + 30 22 ) ( 13 x - 30 22 )}{x ^{2} + 400} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 20 ( 13 x + 30 22 ) ( 13 x - 30 22 ) ) ( - 1 )}{x ^{2} + 400} > 0 \cdot (- 1)

Simplify

\frac{20 ( 13 x + 30 22 ) ( 13 x - 30 22 )}{x ^{2} + 400} > 0

Divide both sides by

20

\frac{\frac{20 ( 13 x + 30 22 ) ( 13 x - 30 22 )}{x ^{2} + 400}}{20} > \frac{0}{20}

Simplify

\frac{( 13 x + 30 22 ) ( 13 x - 30 22 )}{x ^{2} + 400} > 0

Identify the intervals

x < - \frac{30 22}{13} or x > \frac{30 22}{13}

5 \geq - 33 c - 61

w + \frac{3}{8} = - \frac{1}{4}

6 x^{2} - 9 x = - 7 x - 4

2 + 4 Y = 0

16 x^{2} - 324

What is (500000)/(x^2+400)<260 ?
The solution to (500000)/(x^2+400)<260 is x<-(30sqrt(22))/(sqrt(13))\lor x>(30sqrt(22))/(sqrt(13))