To determine the quadratic equation equivalent to [tex]\((x+2)^2 + 5(x+2) - 6 = 0\)[/tex], we will make a substitution.
Let's set [tex]\(u = x + 2\)[/tex]. Then, the original equation can be rewritten in terms of [tex]\(u\)[/tex]:
1. Start with the original equation:
[tex]\[
(x+2)^2 + 5(x+2) - 6 = 0
\][/tex]
With [tex]\(u = x + 2\)[/tex], we substitute in place of [tex]\((x + 2)\)[/tex]:
[tex]\[
(u)^2 + 5(u) - 6 = 0
\][/tex]
2. Simplify this equation:
[tex]\[
u^2 + 5u - 6 = 0
\][/tex]
So, the quadratic equation equivalent to [tex]\((x+2)^2 + 5(x+2) - 6 = 0\)[/tex] is:
[tex]\[
u^2 + 5u - 6 = 0
\][/tex]
where [tex]\(u = x + 2\)[/tex].
Therefore, the correct answer is:
[tex]\[
u^2 + 5u - 6 = 0 \quad \text{where } u = (x+2)
\][/tex]
