p^2=2p+99

Solution for p^2=2p+99 equation:

Simplifying
p2 = 2p + 99

Reorder the terms:
p2 = 99 + 2p

Solving
p2 = 99 + 2p

Solving for variable 'p'.

Reorder the terms:
-99 + -2p + p2 = 99 + 2p + -99 + -2p

Reorder the terms:
-99 + -2p + p2 = 99 + -99 + 2p + -2p

Combine like terms: 99 + -99 = 0
-99 + -2p + p2 = 0 + 2p + -2p
-99 + -2p + p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
-99 + -2p + p2 = 0

Factor a trinomial.
(-9 + -1p)(11 + -1p) = 0

Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve:

Simplifying
-9 + -1p = 0

Solving
-9 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + -1p = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1p = 0 + 9
-1p = 0 + 9

Combine like terms: 0 + 9 = 9
-1p = 9

Divide each side by '-1'.
p = -9

Simplifying
p = -9
Subproblem 2
Set the factor '(11 + -1p)' equal to zero and attempt to solve:

Simplifying
11 + -1p = 0

Solving
11 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -1p = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1p = 0 + -11
-1p = 0 + -11

Combine like terms: 0 + -11 = -11
-1p = -11

Divide each side by '-1'.
p = 11

Simplifying
p = 11
Solution
p = {-9, 11}