What is the answer to |x-1|=sqrt(x) ?

The answer to |x-1|=sqrt(x) is x=(3-sqrt(5))/2 \lor x=(3+sqrt(5))/2

Solve for x: |x-1|=sqrt(x)

The solution is x=(3-sqrt(5))/2 \lor x=(3+sqrt(5))/2

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∣ x - 1 ∣ = x

x = \frac{3 - 5}{2} or x = \frac{3 + 5}{2}

Decimal Notation

x = 0.38196 \dots, x = 2.61803 \dots

Solution steps

∣ x - 1 ∣ = x

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

x = \frac{3 - 5}{2} or x = \frac{3 + 5}{2}

2 (x + 12) = - 2 (x - 4)

x^{2} - 4 = 77

(2 x + 1) (x - 4) = 3

3 a^{2} + 22 a - 45

\frac{3 x - 1}{∣ x - 1 ∣} \geq 4

What is the answer to |x-1|=sqrt(x) ?
The answer to |x-1|=sqrt(x) is x=(3-sqrt(5))/2 \lor x=(3+sqrt(5))/2
Solve for x: |x-1|=sqrt(x)
The solution is x=(3-sqrt(5))/2 \lor x=(3+sqrt(5))/2