Sure, let's go through the expression step-by-step:
[tex]\[
[c+7(d-3)]^2 \div 3
\][/tex]
Given the values:
[tex]\[
a = 5,\ b = 3,\ c = 7,\ d = 5
\][/tex]
1. Evaluate the inner part [tex]\(d - 3\)[/tex]:
[tex]\[
d - 3 = 5 - 3 = 2
\][/tex]
2. Multiply the result by 7:
[tex]\[
7(d - 3) = 7 \times 2 = 14
\][/tex]
3. Add the value of [tex]\(c\)[/tex] to the previous result:
[tex]\[
c + 7(d - 3) = 7 + 14 = 21
\][/tex]
4. Square the entire expression:
[tex]\[
[c + 7(d - 3)]^2 = 21^2 = 441
\][/tex]
5. Divide the result by 3:
[tex]\[
\frac{[c + 7(d - 3)]^2}{3} = \frac{441}{3} = 147.0
\][/tex]
So, the detailed step-by-step evaluation of the expression [tex]\([c + 7(d - 3)]^2 \div 3\)[/tex] leads to the final result of:
[tex]\[
\boxed{147.0}
\][/tex]
