Let's solve the equation [tex]\(\sqrt{2x + 4} = 18\)[/tex] step-by-step:
1. Isolate the square root:
[tex]\[
\sqrt{2x + 4} = 18
\][/tex]
2. Square both sides of the equation to eliminate the square root:
[tex]\[
(\sqrt{2x + 4})^2 = 18^2
\][/tex]
3. Simplify both sides:
[tex]\[
2x + 4 = 324
\][/tex]
4. Solve for [tex]\(x\)[/tex] by first isolating the term with [tex]\(x\)[/tex]:
[tex]\[
2x = 324 - 4
\][/tex]
[tex]\[
2x = 320
\][/tex]
5. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{320}{2}
\][/tex]
[tex]\[
x = 160
\][/tex]
6. Check the solution by substituting [tex]\(x = 160\)[/tex] back into the original equation to ensure it satisfies the equation:
[tex]\[
\sqrt{2(160) + 4} = \sqrt{320 + 4} = \sqrt{324} = 18
\][/tex]
This is true, so [tex]\(x = 160\)[/tex] is a valid solution.
Therefore, the solution to the equation [tex]\(\sqrt{2x + 4} = 18\)[/tex] is [tex]\(x = 160\)[/tex].
