Solve 5(x-3)^2 4=129

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{30 - 645}{10}, x_{2} = \frac{30 + 645}{10}

Alternative Form

x_{1} \approx 0.460315, x_{2} \approx 5.539685

Evaluate

5 (x - 3)^{2} \times 4 = 129

Multiply the terms

20 (x - 3)^{2} = 129

Expand the expression

More Steps

20 x^{2} - 120 x + 180 = 129

Move the expression to the left side

20 x^{2} - 120 x + 51 = 0

Substitute a= 20,b= - 120 and c= 51 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{120 \pm ( - 120 ) ^{2} - 4 \times 20 \times 51}{2 \times 20}

Simplify the expression

x = \frac{120 \pm ( - 120 ) ^{2} - 4 \times 20 \times 51}{40}

Simplify the expression

More Steps

x = \frac{120 \pm 10320}{40}

Simplify the radical expression

More Steps

x = \frac{120 \pm 4 645}{40}

Separate the equation into 2 possible cases

x = \frac{120 + 4 645}{40} x = \frac{120 - 4 645}{40}

Simplify the expression

More Steps

x = \frac{30 + 645}{10} x = \frac{120 - 4 645}{40}

Simplify the expression

More Steps

x = \frac{30 + 645}{10} x = \frac{30 - 645}{10}

Solution

x_{1} = \frac{30 - 645}{10}, x_{2} = \frac{30 + 645}{10}

Alternative Form

x_{1} \approx 0.460315, x_{2} \approx 5.539685

Show Solution