2p^2-4p-28=0

Solution for 2p^2-4p-28=0 equation:

Simplifying
2p2 + -4p + -28 = 0

Reorder the terms:
-28 + -4p + 2p2 = 0

Solving
-28 + -4p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -2p + p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -2p + p2)' equal to zero and attempt to solve:

Simplifying
-14 + -2p + p2 = 0

Solving
-14 + -2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -2p + 14 + p2 = 0 + 14

Reorder the terms:
-14 + 14 + -2p + p2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -2p + p2 = 0 + 14
-2p + p2 = 0 + 14

Combine like terms: 0 + 14 = 14
-2p + p2 = 14

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 = 14 + 1

Reorder the terms:
1 + -2p + p2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + -2p + p2 = 15

Factor a perfect square on the left side:
(p + -1)(p + -1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(p + -1) equal to 3.872983346 and -3.872983346.

Subproblem 1
p + -1 = 3.872983346

Simplifying
p + -1 = 3.872983346

Reorder the terms:
-1 + p = 3.872983346

Solving
-1 + p = 3.872983346

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 = 3.872983346 + 1

Combine like terms: -1 + 1 = 0
0 + p = 3.872983346 + 1
p = 3.872983346 + 1

Combine like terms: 3.872983346 + 1 = 4.872983346
p = 4.872983346

Simplifying
p = 4.872983346

Subproblem 2
p + -1 = -3.872983346

Simplifying
p + -1 = -3.872983346

Reorder the terms:
-1 + p = -3.872983346

Solving
-1 + p = -3.872983346

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 = -3.872983346 + 1

Combine like terms: -1 + 1 = 0
0 + p = -3.872983346 + 1
p = -3.872983346 + 1

Combine like terms: -3.872983346 + 1 = -2.872983346
p = -2.872983346

Simplifying
p = -2.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.872983346, -2.872983346}
Solution
p = {4.872983346, -2.872983346}