What is the answer to |x|=x^2-x ?

The answer to |x|=x^2-x is x=0\lor x=2

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|x|=x^2-x

∣ x ∣ = x^{2} - x

x = 0 or x = 2

Solution steps

∣ x ∣ = x^{2} - x

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

No Solution or (x = 0 or x = 2)

x = 0 or x = 2

2 x - 5 = ∣ x + 4 ∣

∣ 4 x + 3 ∣ = 16

\frac{x}{2} + \frac{1}{3} = 4

x^{2} - 4 + 9 = 5

4 x^{3} - \frac{x}{∣ x ∣} = 0