9p^2-18p-3=-10

Solution for 9p^2-18p-3=-10 equation:

Simplifying
9p2 + -18p + -3 = -10

Reorder the terms:
-3 + -18p + 9p2 = -10

Solving
-3 + -18p + 9p2 = -10

Solving for variable 'p'.

Reorder the terms:
-3 + 10 + -18p + 9p2 = -10 + 10

Combine like terms: -3 + 10 = 7
7 + -18p + 9p2 = -10 + 10

Combine like terms: -10 + 10 = 0
7 + -18p + 9p2 = 0

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

Divide each side by '9'.
0.7777777778 + -2p + p2 = 0

Move the constant term to the right:

Add '-0.7777777778' to each side of the equation.
0.7777777778 + -2p + -0.7777777778 + p2 = 0 + -0.7777777778

Reorder the terms:
0.7777777778 + -0.7777777778 + -2p + p2 = 0 + -0.7777777778

Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000
0.0000000000 + -2p + p2 = 0 + -0.7777777778
-2p + p2 = 0 + -0.7777777778

Combine like terms: 0 + -0.7777777778 = -0.7777777778
-2p + p2 = -0.7777777778

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 = -0.7777777778 + 1

Reorder the terms:
1 + -2p + p2 = -0.7777777778 + 1

Combine like terms: -0.7777777778 + 1 = 0.2222222222
1 + -2p + p2 = 0.2222222222

Factor a perfect square on the left side:
(p + -1)(p + -1) = 0.2222222222

Calculate the square root of the right side: 0.471404521

Break this problem into two subproblems by setting 
(p + -1) equal to 0.471404521 and -0.471404521.

Subproblem 1
p + -1 = 0.471404521

Simplifying
p + -1 = 0.471404521

Reorder the terms:
-1 + p = 0.471404521

Solving
-1 + p = 0.471404521

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 = 0.471404521 + 1

Combine like terms: -1 + 1 = 0
0 + p = 0.471404521 + 1
p = 0.471404521 + 1

Combine like terms: 0.471404521 + 1 = 1.471404521
p = 1.471404521

Simplifying
p = 1.471404521

Subproblem 2
p + -1 = -0.471404521

Simplifying
p + -1 = -0.471404521

Reorder the terms:
-1 + p = -0.471404521

Solving
-1 + p = -0.471404521

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 = -0.471404521 + 1

Combine like terms: -1 + 1 = 0
0 + p = -0.471404521 + 1
p = -0.471404521 + 1

Combine like terms: -0.471404521 + 1 = 0.528595479
p = 0.528595479

Simplifying
p = 0.528595479

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.471404521, 0.528595479}