Question

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

Answer 1

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

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=(5)/(3) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to x=- (8)/(3)\\\\`

The value of p: 9 and -4

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