Solve 3(x - 2)^2 = 24

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 2 - 22, x_{2} = 2 + 22

Alternative Form

x_{1} \approx - 0.828427, x_{2} \approx 4.828427

Evaluate

3 (x - 2)^{2} = 24

Expand the expression

More Steps

3 x^{2} - 12 x + 12 = 24

Move the expression to the left side

3 x^{2} - 12 x - 12 = 0

Substitute a= 3,b= - 12 and c= - 12 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 3 ( - 12 )}{2 \times 3}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 3 ( - 12 )}{6}

Simplify the expression

More Steps

x = \frac{12 \pm 288}{6}

Simplify the radical expression

More Steps

x = \frac{12 \pm 12 2}{6}

Separate the equation into 2 possible cases

x = \frac{12 + 12 2}{6} x = \frac{12 - 12 2}{6}

Simplify the expression

More Steps

x = 2 + 22 x = \frac{12 - 12 2}{6}

Simplify the expression

More Steps

x = 2 + 22 x = 2 - 22

Solution

x_{1} = 2 - 22, x_{2} = 2 + 22

Alternative Form

x_{1} \approx - 0.828427, x_{2} \approx 4.828427

Show Solution