4p^2-8p-44=-3

Solution for 4p^2-8p-44=-3 equation:

Simplifying
4p2 + -8p + -44 = -3

Reorder the terms:
-44 + -8p + 4p2 = -3

Solving
-44 + -8p + 4p2 = -3

Solving for variable 'p'.

Reorder the terms:
-44 + 3 + -8p + 4p2 = -3 + 3

Combine like terms: -44 + 3 = -41
-41 + -8p + 4p2 = -3 + 3

Combine like terms: -3 + 3 = 0
-41 + -8p + 4p2 = 0

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

Divide each side by '4'.
-10.25 + -2p + p2 = 0

Move the constant term to the right:

Add '10.25' to each side of the equation.
-10.25 + -2p + 10.25 + p2 = 0 + 10.25

Reorder the terms:
-10.25 + 10.25 + -2p + p2 = 0 + 10.25

Combine like terms: -10.25 + 10.25 = 0.00
0.00 + -2p + p2 = 0 + 10.25
-2p + p2 = 0 + 10.25

Combine like terms: 0 + 10.25 = 10.25
-2p + p2 = 10.25

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 = 10.25 + 1

Reorder the terms:
1 + -2p + p2 = 10.25 + 1

Combine like terms: 10.25 + 1 = 11.25
1 + -2p + p2 = 11.25

Factor a perfect square on the left side:
(p + -1)(p + -1) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(p + -1) equal to 3.354101966 and -3.354101966.

Subproblem 1
p + -1 = 3.354101966

Simplifying
p + -1 = 3.354101966

Reorder the terms:
-1 + p = 3.354101966

Solving
-1 + p = 3.354101966

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 = 3.354101966 + 1

Combine like terms: -1 + 1 = 0
0 + p = 3.354101966 + 1
p = 3.354101966 + 1

Combine like terms: 3.354101966 + 1 = 4.354101966
p = 4.354101966

Simplifying
p = 4.354101966

Subproblem 2
p + -1 = -3.354101966

Simplifying
p + -1 = -3.354101966

Reorder the terms:
-1 + p = -3.354101966

Solving
-1 + p = -3.354101966

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 = -3.354101966 + 1

Combine like terms: -1 + 1 = 0
0 + p = -3.354101966 + 1
p = -3.354101966 + 1

Combine like terms: -3.354101966 + 1 = -2.354101966
p = -2.354101966

Simplifying
p = -2.354101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.354101966, -2.354101966}