Answer:
The equation is "[tex]\bold{p^2-5p-36=0}[/tex]"
Step-by-step explanation:
Given:
[tex]\to p=3x+4[/tex]
evaluate [tex](3x+4)^2-36=15x+20[/tex] in terms of p=?
[tex]\to (3x+4)^2-36=15x+20\\\\\to (3x+4)^2-36=5(3x+4)\\\\\to p^2-36=5p\\\\[/tex]
Expression in terms of p:
[tex]\to \bold{p^2-5p-36=0}\\\\[/tex]
[tex]\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}\\\\[/tex]
The value of p: 9 and -4
Equation is: [tex]\bold{p^2-5p-36=0}[/tex]
