To evaluate the function [tex]\( h(x) = x^2 - 5x \)[/tex] for the given value of [tex]\( x = q + 5 \)[/tex], follow these steps:
1. Substitute [tex]\( q + 5 \)[/tex] into the function in place of [tex]\( x \)[/tex]:
[tex]\[ h(q + 5) = (q + 5)^2 - 5(q + 5) \][/tex]
2. Expand the squared term [tex]\((q + 5)^2\)[/tex]:
[tex]\[ (q + 5)^2 = q^2 + 10q + 25 \][/tex]
3. Distribute the [tex]\(-5\)[/tex] in the term [tex]\(-5(q + 5)\)[/tex]:
[tex]\[ -5(q + 5) = -5q - 25 \][/tex]
4. Substitute these expanded terms back into the expression:
[tex]\[ h(q + 5) = q^2 + 10q + 25 - 5q - 25 \][/tex]
5. Combine like terms:
[tex]\[ q^2 + 10q + 25 - 5q - 25 = q^2 + 5q \][/tex]
So, the simplified expression for [tex]\( h(q + 5) \)[/tex] is:
[tex]\[ h(q + 5) = q^2 + 5q \][/tex]
