To write an equivalent quadratic equation using substitution, follow these steps:
1. Identify the substitution variable:
Let [tex]\( u = 3x + 2 \)[/tex].
2. Substitute [tex]\( u \)[/tex] into the equation:
Replace [tex]\( 3x + 2 \)[/tex] in the original equation with [tex]\( u \)[/tex].
[tex]\[
(3x + 2)^2 + 7(3x + 2) - 8 = 0
\][/tex]
becomes
[tex]\[
u^2 + 7u - 8 = 0
\][/tex]
3. Write the equivalent quadratic equation:
The new equation, after substitution, is:
[tex]\[
u^2 + 7u - 8 = 0
\][/tex]
So, the equivalent quadratic equation is:
[tex]\[
u^2 + 7u - 8 = 0,
\][/tex]
where [tex]\( u = 3x + 2 \)[/tex].
