Solve 4(x - 1)^2 = 28

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 1 - 7, x_{2} = 1 + 7

Alternative Form

x_{1} \approx - 1.645751, x_{2} \approx 3.645751

Evaluate

4 (x - 1)^{2} = 28

Expand the expression

More Steps

4 x^{2} - 8 x + 4 = 28

Move the expression to the left side

4 x^{2} - 8 x - 24 = 0

Substitute a= 4,b= - 8 and c= - 24 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 4 ( - 24 )}{2 \times 4}

Simplify the expression

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 4 ( - 24 )}{8}

Simplify the expression

More Steps

x = \frac{8 \pm 448}{8}

Simplify the radical expression

More Steps

x = \frac{8 \pm 8 7}{8}

Separate the equation into 2 possible cases

x = \frac{8 + 8 7}{8} x = \frac{8 - 8 7}{8}

Simplify the expression

More Steps

x = 1 + 7 x = \frac{8 - 8 7}{8}

Simplify the expression

More Steps

x = 1 + 7 x = 1 - 7

Solution

x_{1} = 1 - 7, x_{2} = 1 + 7

Alternative Form

x_{1} \approx - 1.645751, x_{2} \approx 3.645751

Show Solution