Solve 3(x-2)^2 4=52

Question

3 (x - 2)^{2} \times 4 = 52

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{6 - 39}{3}, x_{2} = \frac{6 + 39}{3}

Alternative Form

x_{1} \approx - 0.081666, x_{2} \approx 4.081666

Evaluate

3 (x - 2)^{2} \times 4 = 52

Multiply the terms

12 (x - 2)^{2} = 52

Expand the expression

More Steps

12 x^{2} - 48 x + 48 = 52

Move the expression to the left side

12 x^{2} - 48 x - 4 = 0

Substitute a= 12,b= - 48 and c= - 4 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{48 \pm ( - 48 ) ^{2} - 4 \times 12 ( - 4 )}{2 \times 12}

Simplify the expression

x = \frac{48 \pm ( - 48 ) ^{2} - 4 \times 12 ( - 4 )}{24}

Simplify the expression

More Steps

x = \frac{48 \pm 2496}{24}

Simplify the radical expression

More Steps

x = \frac{48 \pm 8 39}{24}

Separate the equation into 2 possible cases

x = \frac{48 + 8 39}{24} x = \frac{48 - 8 39}{24}

Simplify the expression

More Steps

x = \frac{6 + 39}{3} x = \frac{48 - 8 39}{24}

Simplify the expression

More Steps

x = \frac{6 + 39}{3} x = \frac{6 - 39}{3}

Solution

x_{1} = \frac{6 - 39}{3}, x_{2} = \frac{6 + 39}{3}

Alternative Form

x_{1} \approx - 0.081666, x_{2} \approx 4.081666

Show Solution