What is the answer to |x^2-2x|+x=6 ?

The answer to |x^2-2x|+x=6 is x=-2\lor x=3

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|x^2-2x|+x=6

x^{2} - 2 x + x = 6

x = - 2 or x = 3

Solution steps

x^{2} - 2 x + x = 6

Find positive and negative intervals

x \leq 0, 0 < x < 2, x \geq 2

Solve the inequality for each interval

x = - 2 or No Solution or x = 3

x = - 2 or x = 3

∣ 3 x + 2 ∣ = ∣ x - 6 ∣

∣ x - 8 ∣ = 8

x^{2} - 4 x + 7 = 2 x^{2} - 3 x + 5

∣ 10 x + 9 ∣ = 18

x^{2} - 4 x = - 5