Question

Solve by completing the square: 8x^2+16x=42 Please show steps

Answer 1

Hi,

Equation:

$8 {x}^{2} + 16x = 42$

Work:

Divide both sides of equation with 2.

$4 {x}^{2} + 8x = 21$

Move constant 21 to the left and change its sign.

$4 {x}^{2} + 8x - 21 = 0$

Write 8x as a difference.

$4 {x}^{2} + 14x - 6x - 21 = 0$

Factor out 2x from the expression.

$2x \times (2x + 7) - 6x - 21 = 0$

Factor out 2x + 7 from the expression.

$2x \times (2x + 7) - 3(2x + 7) = 0 \\ (2x + 7) \times (2x - 3) = 0$

When the product of factors is 0, at least one factor is 0.

$2x + 7 = 0 \\ 2x - 3 = 0$

Solve equation for x.

$x = - \frac{7}{2} \\ 2x -3 = 0 \\ x = \frac{3}{2}$

The final solutions are:

$x = - \frac{7}{2} \: and \: y = \frac{3}{2}$

Hope this helps.
r3t40