What is the answer to |x-5|=x^2-5x ?

The answer to |x-5|=x^2-5x is x=-1\lor x=5

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|x-5|=x^2-5x

∣ x - 5 ∣ = x^{2} - 5 x

x = - 1 or x = 5

Solution steps

∣ x - 5 ∣ = x^{2} - 5 x

Find positive and negative intervals

x < 5, x \geq 5

Solve the inequality for each interval

x = - 1 or x = 5

- 9 + 2 ∣ x - 6 ∣ = 7

∣ 2 x + 9 ∣ = 4 x

10 - 4 ∣ 2 x - 10 ∣ = 20

∣ m + 2 ∣ = 4

∣ m + 2 ∣ = 0