Question

question
solve for x:
\\(\sqrt{8x - 39} + 12 = 13\\)
answer
attempt 1 out of 2
\\(x = \square\\) submit answer

Explanation:

Step1: Isolate the square root term

Subtract 12 from both sides of the equation $\sqrt{8x - 39}+12 = 13$.
$\sqrt{8x - 39}+12-12=13 - 12$
$\sqrt{8x - 39}=1$

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{8x - 39}=1$.
$(\sqrt{8x - 39})^2=1^2$
$8x-39 = 1$

Step3: Solve for x

Add 39 to both sides: $8x-39 + 39=1 + 39$
$8x=40$
Divide both sides by 8: $\frac{8x}{8}=\frac{40}{8}$
$x = 5$

Step4: Check the solution (optional but recommended)

Substitute $x = 5$ into the original equation:
Left - hand side: $\sqrt{8\times5-39}+12=\sqrt{40 - 39}+12=\sqrt{1}+12=1 + 12=13$, which is equal to the right - hand side. So the solution is valid.

Answer:

$x = 5$