Solve (3x-1)2 - 8(x 1)2 = (2 x)(x-2)

Question

(3 x - 1) \times 2 - 8 (x \times 1) \times 2 = 2 x (x - 2)

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{3 + 5}{2}, x_{2} = \frac{- 3 + 5}{2}

Alternative Form

x_{1} \approx - 2.618034, x_{2} \approx - 0.381966

Evaluate

(3 x - 1) \times 2 - 8 (x \times 1) \times 2 = 2 x (x - 2)

Remove the parentheses

(3 x - 1) \times 2 - 8 x \times 1 \times 2 = 2 x (x - 2)

Simplify

More Steps

2 (3 x - 1) - 16 x = 2 x (x - 2)

Swap the sides

2 x (x - 2) = 2 (3 x - 1) - 16 x

Expand the expression

More Steps

2 x^{2} - 4 x = 2 (3 x - 1) - 16 x

Expand the expression

More Steps

2 x^{2} - 4 x = - 10 x - 2

Move the expression to the left side

2 x^{2} + 6 x + 2 = 0

Substitute a= 2,b= 6 and c= 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 6 \pm 6 ^{2} - 4 \times 2 \times 2}{2 \times 2}

Simplify the expression

x = \frac{- 6 \pm 6 ^{2} - 4 \times 2 \times 2}{4}

Simplify the expression

More Steps

x = \frac{- 6 \pm 20}{4}

Simplify the radical expression

More Steps

x = \frac{- 6 \pm 2 5}{4}

Separate the equation into 2 possible cases

x = \frac{- 6 + 2 5}{4} x = \frac{- 6 - 2 5}{4}

Simplify the expression

More Steps

x = \frac{- 3 + 5}{2} x = \frac{- 6 - 2 5}{4}

Simplify the expression

More Steps

x = \frac{- 3 + 5}{2} x = - \frac{3 + 5}{2}

Solution

x_{1} = - \frac{3 + 5}{2}, x_{2} = \frac{- 3 + 5}{2}

Alternative Form

x_{1} \approx - 2.618034, x_{2} \approx - 0.381966

Show Solution