To solve the given expression [tex]\(5(x-6+3x)^2-6\)[/tex] for [tex]\(x = 2\)[/tex], follow these steps:
1. Substitute [tex]\(x = 2\)[/tex] into the expression:
[tex]\[
5(2 - 6 + 3 \cdot 2)^2 - 6
\][/tex]
2. Simplify inside the parentheses:
[tex]\[
2 - 6 + 3 \cdot 2
\][/tex]
3. Calculate [tex]\(3 \cdot 2\)[/tex]:
[tex]\[
3 \cdot 2 = 6
\][/tex]
4. Continue simplifying inside the parentheses:
[tex]\[
2 - 6 + 6
\][/tex]
[tex]\[
2 - 6 + 6 = 2
\][/tex]
5. Now we have:
[tex]\[
5(2)^2 - 6
\][/tex]
6. Calculate [tex]\((2)^2\)[/tex]:
[tex]\[
(2)^2 = 4
\][/tex]
7. Multiply by 5:
[tex]\[
5 \cdot 4 = 20
\][/tex]
8. Subtract 6:
[tex]\[
20 - 6 = 14
\][/tex]
Therefore, the value of the expression [tex]\(5(x-6+3x)^2-6\)[/tex] when [tex]\(x = 2\)[/tex] is [tex]\(14\)[/tex].
The correct answer is (b) [tex]\(14\)[/tex].
