4p^2-8p-9=0

Solution for 4p^2-8p-9=0 equation:

Simplifying
4p2 + -8p + -9 = 0

Reorder the terms:
-9 + -8p + 4p2 = 0

Solving
-9 + -8p + 4p2 = 0

Solving for variable 'p'.

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

Divide each side by '4'.
-2.25 + -2p + p2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -2p + 2.25 + p2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -2p + p2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -2p + p2 = 0 + 2.25
-2p + p2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-2p + p2 = 2.25

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 = 2.25 + 1

Reorder the terms:
1 + -2p + p2 = 2.25 + 1

Combine like terms: 2.25 + 1 = 3.25
1 + -2p + p2 = 3.25

Factor a perfect square on the left side:
(p + -1)(p + -1) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(p + -1) equal to 1.802775638 and -1.802775638.

Subproblem 1
p + -1 = 1.802775638

Simplifying
p + -1 = 1.802775638

Reorder the terms:
-1 + p = 1.802775638

Solving
-1 + p = 1.802775638

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 = 1.802775638 + 1

Combine like terms: -1 + 1 = 0
0 + p = 1.802775638 + 1
p = 1.802775638 + 1

Combine like terms: 1.802775638 + 1 = 2.802775638
p = 2.802775638

Simplifying
p = 2.802775638

Subproblem 2
p + -1 = -1.802775638

Simplifying
p + -1 = -1.802775638

Reorder the terms:
-1 + p = -1.802775638

Solving
-1 + p = -1.802775638

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 = -1.802775638 + 1

Combine like terms: -1 + 1 = 0
0 + p = -1.802775638 + 1
p = -1.802775638 + 1

Combine like terms: -1.802775638 + 1 = -0.802775638
p = -0.802775638

Simplifying
p = -0.802775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.802775638, -0.802775638}