What is the answer to |x^2-2|=2-3x ?

The answer to |x^2-2|=2-3x is x=-4\lor x=0

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|x^2-2|=2-3x

x^{2} - 2 = 2 - 3 x

x = - 4 or x = 0

Solution steps

x^{2} - 2 = 2 - 3 x

Find positive and negative intervals

x \leq - 2, - 2 < x < 2, x \geq 2

Solve the inequality for each interval

x = - 4 or x = 0 or No Solution

x = - 4 or x = 0

12 + 3 ∣ x + 3 ∣ = 9 x - 9

∣ 1 - 2 x ∣ = - 2 x

- 14 ∣ 3 x + 6 ∣ = - 28

x^{2} + 1 - x^{2} - 1 = 0

x^{2} - 9 = x - 3