To find the value of the expression [tex]\(\left|m^2 - 7\right| + n^2\)[/tex] when [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex], we need to perform the following steps:
1. Calculate [tex]\(m^2\)[/tex]:
[tex]\[
m = -2 \implies m^2 = (-2)^2 = 4
\][/tex]
2. Calculate [tex]\(n^2\)[/tex]:
[tex]\[
n = 5 \implies n^2 = 5^2 = 25
\][/tex]
3. Compute [tex]\(m^2 - 7\)[/tex]:
[tex]\[
m^2 - 7 = 4 - 7 = -3
\][/tex]
4. Take the absolute value of [tex]\((m^2 - 7)\)[/tex]:
[tex]\[
\left|m^2 - 7\right| = \left|-3\right| = 3
\][/tex]
5. Finally, add the absolute value to [tex]\(n^2\)[/tex]:
[tex]\[
\left|m^2 - 7\right| + n^2 = 3 + 25 = 28
\][/tex]
So, the value of the expression when [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex] is [tex]\(\boxed{28}\)[/tex].
