To solve the expression [tex]\( \left|m^2 - 7\right| + n^2 \)[/tex] when [tex]\( m = -2 \)[/tex] and [tex]\( n = 5 \)[/tex], follow these steps:
1. Calculate [tex]\( m^2 \)[/tex]:
Given [tex]\( m = -2 \)[/tex],
[tex]\[
m^2 = (-2)^2 = 4
\][/tex]
2. Calculate [tex]\( n^2 \)[/tex]:
Given [tex]\( n = 5 \)[/tex],
[tex]\[
n^2 = 5^2 = 25
\][/tex]
3. Substitute [tex]\( m^2 \)[/tex] into the expression:
Since [tex]\( m^2 = 4 \)[/tex],
[tex]\[
\left|4 - 7\right|
\][/tex]
4. Calculate the absolute value:
[tex]\[
4 - 7 = -3
\][/tex]
[tex]\[
\left|-3\right| = 3
\][/tex]
5. Add [tex]\( n^2 \)[/tex]:
[tex]\[
3 + 25 = 28
\][/tex]
Hence, the value of the expression when [tex]\( m = -2 \)[/tex] and [tex]\( n = 5 \)[/tex] is [tex]\( 28 \)[/tex].
