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Use substitution to write an equivalent quadratic equation:

[tex]\[
(3x + 2)^2 + 7(3x + 2) - 8 = 0
\][/tex]

Sagot :

GinnyAnswer
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].
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