What is the answer to |x^2+2|=2x+1 ?

The answer to |x^2+2|=2x+1 is x=1

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|x^2+2|=2x+1

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

x = 1

Solution steps

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

Find positive and negative intervals

- \infty < x < \infty

Solve the inequality for each interval

x = 1

- 3 ∣ 4 x - 9 ∣ = 24

- 7 = \frac{∣ a - 3 ∣}{- 2}

∣ 2 x + 6 ∣ = 4 x

5 ∣ q + 6 ∣ = 20

∣ - 9 + a ∣ = 1