You could make this problem simpler by dividing all 4 terms by 50:
p^2 - 52p - 450 = 0
To solve this we could use any of the following:
graphing
completing the square
quadratic formula
factoring
I'll use the quadratic formula. Here, a=1, b= -52 and c = -450.
-(-52) plus or minus sqrt( [-52]^2 - 4(1)(-450)
Then x = -------------------------------------------------------------
2
52 plus or minus sqrt(4504)
This simplifies to x = -----------------------------------------
2
Unfortunately, the answers are not "nice."
52 plus or minus 67.11
x = ----------------------------------
2
Can you simplify these results further?
If I try completing the square, I obtain from p^2 - 52p - 450 the following:
p^2 - 52p + (-26)^2 - (-26)^2 - 450 = 0 => (p-26)^2 - 676 - 450 = 0.
This results in (p-26)^2 - 1126 = 0, or
(p-26)^2 = 1126
Then p-26 = plus or minus 33.56, or
p = 26 plus or minus 33.56.