Solve 7 (x-4)^(2)=11

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{28 - 77}{7}, x_{2} = \frac{28 + 77}{7}

Alternative Form

x_{1} \approx 2.746434, x_{2} \approx 5.253566

Evaluate

7 (x - 4)^{2} = 11

Expand the expression

More Steps

7 x^{2} - 56 x + 112 = 11

Move the expression to the left side

7 x^{2} - 56 x + 101 = 0

Substitute a= 7,b= - 56 and c= 101 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{56 \pm ( - 56 ) ^{2} - 4 \times 7 \times 101}{2 \times 7}

Simplify the expression

x = \frac{56 \pm ( - 56 ) ^{2} - 4 \times 7 \times 101}{14}

Simplify the expression

More Steps

x = \frac{56 \pm 308}{14}

Simplify the radical expression

More Steps

x = \frac{56 \pm 2 77}{14}

Separate the equation into 2 possible cases

x = \frac{56 + 2 77}{14} x = \frac{56 - 2 77}{14}

Simplify the expression

More Steps

x = \frac{28 + 77}{7} x = \frac{56 - 2 77}{14}

Simplify the expression

More Steps

x = \frac{28 + 77}{7} x = \frac{28 - 77}{7}

Solution

x_{1} = \frac{28 - 77}{7}, x_{2} = \frac{28 + 77}{7}

Alternative Form

x_{1} \approx 2.746434, x_{2} \approx 5.253566

Show Solution