What is 2x^3-72x<x^2-36 ?

The solution to 2x^3-72x<x^2-36 is x<-6\lor 1/2 <x<6

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2x^3-72x<x^2-36

2 x^{3} - 72 x < x^{2} - 36

x < - 6 or \frac{1}{2} < x < 6

Interval Notation

(- \infty, - 6) \cup (\frac{1}{2}, 6)

Decimal Notation

x < - 6 or 0.5 < x < 6

Solution steps

2 x^{3} - 72 x < x^{2} - 36

Rewrite in standard form

2 x^{3} - 72 x + 36 - x^{2} < 0

Factor

2 x^{3} - 72 x + 36 - x^{2} : (2 x - 1) (x + 6) (x - 6)

(2 x - 1) (x + 6) (x - 6) < 0

Identify the intervals

x < - 6 or \frac{1}{2} < x < 6

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

x^{2} - 18 x = 0

\frac{2}{- 5}

- 2 + 3 (1) \geq \frac{1}{3}

6 x^{2} - 18 x + 12 = 0