Question

square root functions and equations
what is the solution of \\(\sqrt{x + 2} - 15 = -3\\)?
\\(x = 142\\)
\\(x = 232\\)
\\(x = 322\\)
no solution

Explanation:

Step1: Isolate the square root term

Add 15 to both sides of the equation \(\sqrt{x + 2}-15=-3\) to isolate the square root term.
\(\sqrt{x + 2}=-3 + 15\)
\(\sqrt{x + 2}=12\)

Step2: Square both sides to eliminate the square root

Square both sides of the equation \(\sqrt{x + 2}=12\) to get rid of the square root.
\((\sqrt{x + 2})^2=12^2\)
\(x + 2 = 144\)

Step3: Solve for x

Subtract 2 from both sides of the equation \(x + 2 = 144\) to solve for x.
\(x=144 - 2\)
\(x = 142\)

Step4: Check the solution

Substitute \(x = 142\) back into the original equation \(\sqrt{x + 2}-15=-3\) to check if it is a valid solution.
Left - hand side: \(\sqrt{142+2}-15=\sqrt{144}-15 = 12-15=-3\)
Right - hand side: \(-3\)
Since the left - hand side equals the right - hand side, \(x = 142\) is a valid solution.

Answer:

\(x = 142\) (i.e., the option with \(x = 142\))