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}
