Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$4(x + 2)^2 - 46 = -18$
answer attempt 1 out of 2
additional solution no solution
$x = $
submit answer
$\pm$ $\sqrt{}$

Explanation:

Step1: Isolate the squared term

Add 46 to both sides:
$4(x+2)^2 = -18 + 46$
$4(x+2)^2 = 28$

Step2: Simplify the equation

Divide both sides by 4:
$(x+2)^2 = \frac{28}{4}$
$(x+2)^2 = 7$

Step3: Take square roots of both sides

Apply square root property:
$x+2 = \pm\sqrt{7}$

Step4: Solve for x

Subtract 2 from both sides:
$x = -2 \pm\sqrt{7}$

Answer:

$x=-2+\sqrt{7}$ and $x=-2-\sqrt{7}$