Solve 4(x-1)^2 2=10

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{2 - 5}{2}, x_{2} = \frac{2 + 5}{2}

Alternative Form

x_{1} \approx - 0.118034, x_{2} \approx 2.118034

Evaluate

4 (x - 1)^{2} \times 2 = 10

Multiply the terms

8 (x - 1)^{2} = 10

Expand the expression

More Steps

8 x^{2} - 16 x + 8 = 10

Move the expression to the left side

8 x^{2} - 16 x - 2 = 0

Substitute a= 8,b= - 16 and c= - 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 8 ( - 2 )}{2 \times 8}

Simplify the expression

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 8 ( - 2 )}{16}

Simplify the expression

More Steps

x = \frac{16 \pm 320}{16}

Simplify the radical expression

More Steps

x = \frac{16 \pm 8 5}{16}

Separate the equation into 2 possible cases

x = \frac{16 + 8 5}{16} x = \frac{16 - 8 5}{16}

Simplify the expression

More Steps

x = \frac{2 + 5}{2} x = \frac{16 - 8 5}{16}

Simplify the expression

More Steps

x = \frac{2 + 5}{2} x = \frac{2 - 5}{2}

Solution

x_{1} = \frac{2 - 5}{2}, x_{2} = \frac{2 + 5}{2}

Alternative Form

x_{1} \approx - 0.118034, x_{2} \approx 2.118034

Show Solution