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Simplifying
p2 + -0.75p + 0.125 = 0

Reorder the terms:
0.125 + -0.75p + p2 = 0

Solving
0.125 + -0.75p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -0.75p + -0.125 + p2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -0.75p + p2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -0.75p + p2 = 0 + -0.125
-0.75p + p2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-0.75p + p2 = -0.125

The p term is -0.75p.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75p + 0.140625 + p2 = -0.125 + 0.140625

Reorder the terms:
0.140625 + -0.75p + p2 = -0.125 + 0.140625

Combine like terms: -0.125 + 0.140625 = 0.015625
0.140625 + -0.75p + p2 = 0.015625

Factor a perfect square on the left side:
(p + -0.375)(p + -0.375) = 0.015625

Calculate the square root of the right side: 0.125

Break this problem into two subproblems by setting 
(p + -0.375) equal to 0.125 and -0.125.

Subproblem 1

p + -0.375 = 0.125 Simplifying p + -0.375 = 0.125 Reorder the terms: -0.375 + p = 0.125 Solving -0.375 + p = 0.125 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + p = 0.125 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + p = 0.125 + 0.375 p = 0.125 + 0.375 Combine like terms: 0.125 + 0.375 = 0.5 p = 0.5 Simplifying p = 0.5

Subproblem 2

p + -0.375 = -0.125 Simplifying p + -0.375 = -0.125 Reorder the terms: -0.375 + p = -0.125 Solving -0.375 + p = -0.125 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + p = -0.125 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + p = -0.125 + 0.375 p = -0.125 + 0.375 Combine like terms: -0.125 + 0.375 = 0.25 p = 0.25 Simplifying p = 0.25

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.5, 0.25}
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