To solve the equation [tex]\(\sqrt{2x + 4} = 16\)[/tex], we'll follow these steps:
1. Isolate the square root:
[tex]\[
\sqrt{2x + 4} = 16
\][/tex]
2. Eliminate the square root by squaring both sides:
[tex]\[
(\sqrt{2x + 4})^2 = 16^2
\][/tex]
This simplifies to:
[tex]\[
2x + 4 = 256
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
2x + 4 = 256
\][/tex]
Subtract 4 from both sides:
[tex]\[
2x = 252
\][/tex]
Divide both sides by 2:
[tex]\[
x = 126
\][/tex]
Therefore, the solution to the equation [tex]\(\sqrt{2x+4}=16\)[/tex] is [tex]\(x=126\)[/tex].
