P^2=10-9P

Solution for P^2=10-9P equation:

Simplifying
P2 = 10 + -9P

Solving
P2 = 10 + -9P

Solving for variable 'P'.

Reorder the terms:
-10 + 9P + P2 = 10 + -9P + -10 + 9P

Reorder the terms:
-10 + 9P + P2 = 10 + -10 + -9P + 9P

Combine like terms: 10 + -10 = 0
-10 + 9P + P2 = 0 + -9P + 9P
-10 + 9P + P2 = -9P + 9P

Combine like terms: -9P + 9P = 0
-10 + 9P + P2 = 0

Factor a trinomial.
(-10 + -1P)(1 + -1P) = 0

Subproblem 1
Set the factor '(-10 + -1P)' equal to zero and attempt to solve:

Simplifying
-10 + -1P = 0

Solving
-10 + -1P = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1P = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1P = 0 + 10
-1P = 0 + 10

Combine like terms: 0 + 10 = 10
-1P = 10

Divide each side by '-1'.
P = -10

Simplifying
P = -10
Subproblem 2
Set the factor '(1 + -1P)' equal to zero and attempt to solve:

Simplifying
1 + -1P = 0

Solving
1 + -1P = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1P = 0 + -1
-1P = 0 + -1

Combine like terms: 0 + -1 = -1
-1P = -1

Divide each side by '-1'.
P = 1

Simplifying
P = 1
Solution
P = {-10, 1}