Solve (x-2)^2-1=2(x-3)^2-2

Question

(x - 2)^{2} - 1 = 2 (x - 3)^{2} - 2

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 4 - 3, x_{2} = 4 + 3

Alternative Form

x_{1} \approx 2.267949, x_{2} \approx 5.732051

Evaluate

(x - 2)^{2} - 1 = 2 (x - 3)^{2} - 2

Expand the expression

More Steps

x^{2} - 4 x + 3 = 2 (x - 3)^{2} - 2

Expand the expression

More Steps

x^{2} - 4 x + 3 = 2 x^{2} - 12 x + 16

Move the expression to the left side

- x^{2} + 8 x - 13 = 0

Multiply both sides

x^{2} - 8 x + 13 = 0

Substitute a= 1,b= - 8 and c= 13 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 13}{2}

Simplify the expression

More Steps

x = \frac{8 \pm 12}{2}

Simplify the radical expression

More Steps

x = \frac{8 \pm 2 3}{2}

Separate the equation into 2 possible cases

x = \frac{8 + 2 3}{2} x = \frac{8 - 2 3}{2}

Simplify the expression

More Steps

x = 4 + 3 x = \frac{8 - 2 3}{2}

Simplify the expression

More Steps

x = 4 + 3 x = 4 - 3

Solution

x_{1} = 4 - 3, x_{2} = 4 + 3

Alternative Form

x_{1} \approx 2.267949, x_{2} \approx 5.732051

Show Solution