Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$2(x+1)^2 + 30 = 32$
answer attempt 1 out of 2
⚪ additional solution ⚪ no solution
$x = $

Explanation:

Step1: Isolate the squared term

Subtract 30 from both sides:
$2(x+1)^2 = 32 - 30$
$2(x+1)^2 = 2$

Step2: Simplify the equation

Divide both sides by 2:
$(x+1)^2 = \frac{2}{2}$
$(x+1)^2 = 1$

Step3: Take square roots of both sides

$\sqrt{(x+1)^2} = \pm\sqrt{1}$
$x+1 = \pm1$

Step4: Solve for x

Case 1 (positive root):
$x+1 = 1$
$x = 1 - 1$
$x=0$

Case 2 (negative root):
$x+1 = -1$
$x = -1 - 1$
$x=-2$

Answer:

$x=0$ and $x=-2$