Solve |x-1| =sqrtx

Evaluate

∣ x - 1 ∣ = x

Find the domain

∣ x - 1 ∣ = x, x \geq 0

Swap the sides

x = ∣ x - 1 ∣

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(x)^{2} = ∣ x - 1 ∣^{2}

Evaluate the power

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

Move the expression to the left side

x - (x^{2} - 2 x + 1) = 0

Subtract the terms

More Steps

3 x - x^{2} - 1 = 0

Rewrite in standard form

- x^{2} + 3 x - 1 = 0

Multiply both sides

x^{2} - 3 x + 1 = 0

Substitute a= 1,b= - 3 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4}{2}

Simplify the expression

More Steps

x = \frac{3 \pm 5}{2}

Separate the equation into 2 possible cases

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

Check if the solution is in the defined range

x = \frac{3 + 5}{2} x = \frac{3 - 5}{2}, x \geq 0

Find the intersection of the solution and the defined range

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

Check the solution

More Steps

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

Check the solution

More Steps

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

Solution

x_{1} = \frac{3 - 5}{2}, x_{2} = \frac{3 + 5}{2}

Alternative Form

x_{1} \approx 0.381966, x_{2} \approx 2.618034

Solve the equation