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

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

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x^2+|x|=6

x^{2} + ∣ x ∣ = 6

x = - 2 or x = 2

Solution steps

x^{2} + ∣ x ∣ = 6

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x = - 2 or x = 2

z^{4} = ∣ z ∣^{2} + 2

x^{2} - 3 ∣ x ∣ + 4 = 0

2 + ∣ 3 x - 3 ∣ = 2 x + 3

∣ 3 x + 2 ∣ = x - 6

x^{2} = ∣ 2 x - 8 ∣