What is the answer to 4|x|=5-x^2 ?

The answer to 4|x|=5-x^2 is x=-1\lor x=1

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4|x|=5-x^2

4 ∣ x ∣ = 5 - x^{2}

x = - 1 or x = 1

Solution steps

4 ∣ x ∣ = 5 - x^{2}

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x = - 1 or x = 1

x + \frac{5}{4} = \frac{3}{4} x

∣ x + 4 ∣ = ∣ x - 1 ∣

4 x + 12 = x + 20

x^{2} + (x + 7)^{2} = (x + 8)^{2}

\frac{20 - 40 ( 5 )}{5 ^{2}} + \frac{1}{2}