To find the value of the expression [tex]\(\left|m^2 - 7\right| + n^2\)[/tex] for [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex], follow these steps:
1. First, substitute [tex]\(m = -2\)[/tex] into [tex]\(m^2\)[/tex]:
[tex]\[
m^2 = (-2)^2 = 4
\][/tex]
2. Next, substitute [tex]\(m^2 = 4\)[/tex] into [tex]\(\left|m^2 - 7\right|\)[/tex]:
[tex]\[
\left|4 - 7\right| = \left|-3\right| = 3
\][/tex]
3. Then, substitute [tex]\(n = 5\)[/tex] into [tex]\(n^2\)[/tex]:
[tex]\[
n^2 = 5^2 = 25
\][/tex]
4. Finally, add the two results from the previous steps:
[tex]\[
3 + 25 = 28
\][/tex]
So, when [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex], the value of the expression is [tex]\( \boxed{28} \)[/tex].
