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

The answer to |x^2-x-6|=x+2 is x=-2\lor x=2\lor x=4

Solve for x: |x^2-x-6|=x+2

The solution is x=-2\lor x=2\lor x=4

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

x = - 2 or x = 2 or x = 4

Solution steps

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

Find positive and negative intervals

x \leq - 2, - 2 < x < 3, x \geq 3

Solve the inequality for each interval

x = - 2 or x = 2 or x = 4

∣ x - 3 ∣ + ∣ 4 - x ∣ = 1

∣ x + 2 ∣ = 2 (3 - x)

∣ x - 1 ∣ + ∣ x - 3 ∣ = 2

(x + 1) (∣ x ∣ - 1) = \frac{- 1}{2}

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

What is the answer to |x^2-x-6|=x+2 ?
The answer to |x^2-x-6|=x+2 is x=-2\lor x=2\lor x=4
Solve for x: |x^2-x-6|=x+2
The solution is x=-2\lor x=2\lor x=4