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

The answer to |2x-3|=x^2 is x=-3\lor x=1

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|2x-3|=x^2

∣ 2 x - 3 ∣ = x^{2}

x = - 3 or x = 1

Solution steps

∣ 2 x - 3 ∣ = x^{2}

Find positive and negative intervals

x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

(x = - 3 or x = 1) or No Solution

x = - 3 or x = 1

∣ 2 x + 3 ∣ - x = 2

∣ x - 4 ∣ + 2 = 2 x

\frac{a}{7} = 3

∣ 3 x - 1 ∣ - 1 = 4 x

∣ 2 x - 1 ∣ = 4 - x^{2}