Question

which equation is equivalent to $(x^2 - 2)^2 + 18 = 9x^2 - 18$ (assuming substitution with $p$, likely $p = x^2 - 2$ or similar)?
choose 1 answer:
a $p^2 + 9p + 36 = 0$
b $p^2 - 9p + 18 = 0$
c $p^2 - 9p + 36 = 0$
d $p^2 + 9p + 18 = 0$

Explanation:

Step1: Let \( p = x^2 - 2 \)

We substitute \( p \) into the original equation \((x^2 - 2)^2 + 18 = 9x^2 - 18\). First, rewrite \( 9x^2 - 18 \) as \( 9(x^2 - 2) \). So the equation becomes \( p^2 + 18 = 9p \).

Step2: Rearrange the equation

Move all terms to one side to get a quadratic equation in standard form. Subtract \( 9p \) from both sides: \( p^2 - 9p + 18 = 0 \).

Answer:

B. \( p^2 - 9p + 18 = 0 \)