Question

a. 8x² + 8x + 10 = 8

Explanation:

Step1: Rearrange to standard quadratic form

Subtract 8 from both sides:
$8x^2 + 8x + 10 - 8 = 0$
$8x^2 + 8x + 2 = 0$

Step2: Simplify the equation

Divide all terms by 2:
$\frac{8x^2}{2} + \frac{8x}{2} + \frac{2}{2} = 0$
$4x^2 + 4x + 1 = 0$

Step3: Factor the quadratic

Recognize perfect square trinomial:
$(2x + 1)^2 = 0$

Step4: Solve for x

Set the factor equal to 0:
$2x + 1 = 0$
$2x = -1$
$x = -\frac{1}{2}$

Answer:

$x = -\frac{1}{2}$ (repeated root)