Certainly! Let's solve the given equation [tex]\((4x - 16)^{1/2} = 36\)[/tex] step by step to find the value of [tex]\(x\)[/tex].
1. Start with the given equation:
[tex]\[
(4x - 16)^{1/2} = 36
\][/tex]
2. To eliminate the square root, square both sides of the equation:
[tex]\[
(4x - 16)^{1/2}^2 = 36^2
\][/tex]
Simplifying this, we get:
[tex]\[
4x - 16 = 36^2
\][/tex]
3. Calculate [tex]\(36^2\)[/tex]:
[tex]\[
36^2 = 1296
\][/tex]
4. Substitute this back into the equation:
[tex]\[
4x - 16 = 1296
\][/tex]
5. To isolate [tex]\(x\)[/tex], add 16 to both sides of the equation:
[tex]\[
4x - 16 + 16 = 1296 + 16
\][/tex]
Simplifying this, we obtain:
[tex]\[
4x = 1312
\][/tex]
6. Finally, divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{1312}{4}
\][/tex]
Simplifying this, we find:
[tex]\[
x = 328
\][/tex]
So, the solution to the equation [tex]\((4x - 16)^{1/2} = 36\)[/tex] is [tex]\(x = 328\)[/tex]. The correct option is:
[tex]\[ x = 328 \][/tex]
