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

The solution to (500000)/(x^2+400) 5sqrt(34)

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

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

x < - 534 or x > 534

Interval Notation

(- \infty, - 534) \cup (534, \infty)

Decimal Notation

x < - 29.15475 \dots or x > 29.15475 \dots

Solution steps

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

Rewrite in standard form

\frac{- 400 x ^{2} + 340000}{x ^{2} + 400} < 0

Factor

\frac{- 400 x ^{2} + 340000}{x ^{2} + 400} : \frac{- 400 ( x + 5 34 ) ( x - 5 34 )}{x ^{2} + 400}

\frac{- 400 ( x + 5 34 ) ( x - 5 34 )}{x ^{2} + 400} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 400 ( x + 5 34 ) ( x - 5 34 ) ) ( - 1 )}{x ^{2} + 400} > 0 \cdot (- 1)

Simplify

\frac{400 ( x + 5 34 ) ( x - 5 34 )}{x ^{2} + 400} > 0

Divide both sides by

400

\frac{\frac{400 ( x + 5 34 ) ( x - 5 34 )}{x ^{2} + 400}}{400} > \frac{0}{400}

Simplify

\frac{( x + 5 34 ) ( x - 5 34 )}{x ^{2} + 400} > 0

Identify the intervals

x < - 534 or x > 534

180 = 22 + (x - 5)

2 x^{3} + 4 x^{2} - 30 x

\frac{k ^{2} - 8 k + 16}{k ^{2} - 16}

10 a^{2} + 101 ab + 10 b^{2}

8 \cdot 1 0^{3}

What is (500000)/(x^2+400)<400 ?
The solution to (500000)/(x^2+400)<400 is x<-5sqrt(34)\lor x>5sqrt(34)