Question

solve $4 + \sqrt{x + 2} = 6$

Explanation:

Step1: Isolate the square root term

Subtract 4 from both sides of the equation \(4 + \sqrt{x + 2} = 6\) to get \(\sqrt{x + 2}=6 - 4\). Simplifying the right side gives \(\sqrt{x + 2}=2\).

Step2: Eliminate the square root

Square both sides of the equation \(\sqrt{x + 2}=2\) to obtain \(x + 2 = 2^2\). Calculating the right side, we have \(x + 2 = 4\).

Step3: Solve for x

Subtract 2 from both sides of the equation \(x + 2 = 4\) to get \(x=4 - 2\). Simplifying the right side gives \(x = 2\).

Answer:

\(x = 2\)