Solve (x-3)^(2) = x - 2

Evaluate

(x - 3)^{2} = x - 2

Expand the expression

More Steps

x^{2} - 6 x + 9 = x - 2

Move the expression to the left side

x^{2} - 7 x + 11 = 0

Substitute a= 1,b= - 7 and c= 11 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{7 \pm ( - 7 ) ^{2} - 4 \times 11}{2}

Simplify the expression

More Steps

x = \frac{7 \pm 5}{2}

Separate the equation into 2 possible cases

x = \frac{7 + 5}{2} x = \frac{7 - 5}{2}

Solution

x_{1} = \frac{7 - 5}{2}, x_{2} = \frac{7 + 5}{2}

Alternative Form

x_{1} \approx 2.381966, x_{2} \approx 4.618034

Solve the quadratic equation