10p^2-20p-100=0

Solution for 10p^2-20p-100=0 equation:

Simplifying
10p2 + -20p + -100 = 0

Reorder the terms:
-100 + -20p + 10p2 = 0

Solving
-100 + -20p + 10p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-10 + -2p + p2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-10 + -2p + p2)' equal to zero and attempt to solve:

Simplifying
-10 + -2p + p2 = 0

Solving
-10 + -2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2p + 10 + p2 = 0 + 10

Reorder the terms:
-10 + 10 + -2p + p2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2p + p2 = 0 + 10
-2p + p2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2p + p2 = 10

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 + 1

Reorder the terms:
1 + -2p + p2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2p + p2 = 11

Factor a perfect square on the left side:
(p + -1)(p + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(p + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1
p + -1 = 3.31662479

Simplifying
p + -1 = 3.31662479

Reorder the terms:
-1 + p = 3.31662479

Solving
-1 + p = 3.31662479

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 = 3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + p = 3.31662479 + 1
p = 3.31662479 + 1

Combine like terms: 3.31662479 + 1 = 4.31662479
p = 4.31662479

Simplifying
p = 4.31662479

Subproblem 2
p + -1 = -3.31662479

Simplifying
p + -1 = -3.31662479

Reorder the terms:
-1 + p = -3.31662479

Solving
-1 + p = -3.31662479

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 = -3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + p = -3.31662479 + 1
p = -3.31662479 + 1

Combine like terms: -3.31662479 + 1 = -2.31662479
p = -2.31662479

Simplifying
p = -2.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.31662479, -2.31662479}
Solution
p = {4.31662479, -2.31662479}