Question

Let p=3x+4. Which equation is equivalent to (3x+4)^2-36=15x+20 in terms of p

Answer 1

Answer:

The equation is "$\bold{p^2-5p-36=0}$"

Step-by-step explanation:

Given:

$\to p=3x+4$

evaluate $(3x+4)^2-36=15x+20$ in terms of p=?

$\to (3x+4)^2-36=15x+20\\\\\to (3x+4)^2-36=5(3x+4)\\\\\to p^2-36=5p$

Expression in terms of p:

$\to \bold{p^2-5p-36=0}$

$\to p^2-(9-4)p-36=0\\\\\to p^2-9p+4p-36=0\\\\\to p(p-9)+4(p-9)=0\\\\\to (p-9)(p+4)=0\\\\\to p-9=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to p+4=0\\\\\to \bold{p=9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to p=-4}\\\\\to 3x+4=9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to 3x+4=-4\\\\\to 3x=5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to 3x=-8\\\\\to x=\frac{5}{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to x=- \frac{8}{3}$

The value of p: 9 and -4

Equation is: $\bold{p^2-5p-36=0}$