Question

question
solve for x:
\sqrt{4x - 32} - 16 = -14

Explanation:

Step1: Isolate the square root term

Add 16 to both sides of the equation:
$\sqrt{4x - 32} - 16 + 16 = -14 + 16$
$\sqrt{4x - 32} = 2$

Step2: Eliminate the square root

Square both sides of the equation:
$(\sqrt{4x - 32})^2 = 2^2$
$4x - 32 = 4$

Step3: Solve for x

Add 32 to both sides:
$4x - 32 + 32 = 4 + 32$
$4x = 36$
Divide both sides by 4:
$x = \frac{36}{4}$
$x = 9$

Step4: Check the solution

Substitute $x = 9$ back into the original equation:
Left - hand side: $\sqrt{4\times9 - 32}-16=\sqrt{36 - 32}-16=\sqrt{4}-16 = 2 - 16=-14$
Right - hand side: $-14$
Since the left - hand side equals the right - hand side, $x = 9$ is a valid solution.

Answer:

$x = 9$