9(p-2)p=11

Solution for 9(p-2)p=11 equation:

Simplifying
9(p + -2) * p = 11

Reorder the terms:
9(-2 + p) * p = 11

Reorder the terms for easier multiplication:
9p(-2 + p) = 11
(-2 * 9p + p * 9p) = 11
(-18p + 9p2) = 11

Solving
-18p + 9p2 = 11

Solving for variable 'p'.

Reorder the terms:
-11 + -18p + 9p2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -18p + 9p2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.222222222 + -2p + p2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + -2p + 1.222222222 + p2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + -2p + p2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + -2p + p2 = 0 + 1.222222222
-2p + p2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
-2p + p2 = 1.222222222

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = 1.222222222 + 1

Reorder the terms:
1 + -2p + p2 = 1.222222222 + 1

Combine like terms: 1.222222222 + 1 = 2.222222222
1 + -2p + p2 = 2.222222222

Factor a perfect square on the left side:
(p + -1)(p + -1) = 2.222222222

Calculate the square root of the right side: 1.490711985

Break this problem into two subproblems by setting 
(p + -1) equal to 1.490711985 and -1.490711985.

Subproblem 1
p + -1 = 1.490711985

Simplifying
p + -1 = 1.490711985

Reorder the terms:
-1 + p = 1.490711985

Solving
-1 + p = 1.490711985

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 1.490711985 + 1

Combine like terms: -1 + 1 = 0
0 + p = 1.490711985 + 1
p = 1.490711985 + 1

Combine like terms: 1.490711985 + 1 = 2.490711985
p = 2.490711985

Simplifying
p = 2.490711985

Subproblem 2
p + -1 = -1.490711985

Simplifying
p + -1 = -1.490711985

Reorder the terms:
-1 + p = -1.490711985

Solving
-1 + p = -1.490711985

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -1.490711985 + 1

Combine like terms: -1 + 1 = 0
0 + p = -1.490711985 + 1
p = -1.490711985 + 1

Combine like terms: -1.490711985 + 1 = -0.490711985
p = -0.490711985

Simplifying
p = -0.490711985

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.490711985, -0.490711985}