-0.08p^2+0.02p+0.45=0

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Solution for -0.08p^2+0.02p+0.45=0 equation: 


Simplifying
-0.08p2 + 0.02p + 0.45 = 0

Reorder the terms:
0.45 + 0.02p + -0.08p2 = 0

Solving
0.45 + 0.02p + -0.08p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
-0.08 the coefficient of the squared term: 

Divide each side by '-0.08'.
-5.625 + -0.25p + p2 = 0

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + -0.25p + 5.625 + p2 = 0 + 5.625

Reorder the terms:
-5.625 + 5.625 + -0.25p + p2 = 0 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + -0.25p + p2 = 0 + 5.625
-0.25p + p2 = 0 + 5.625

Combine like terms: 0 + 5.625 = 5.625
-0.25p + p2 = 5.625

The p term is -0.25p.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25p + 0.015625 + p2 = 5.625 + 0.015625

Reorder the terms:
0.015625 + -0.25p + p2 = 5.625 + 0.015625

Combine like terms: 5.625 + 0.015625 = 5.640625
0.015625 + -0.25p + p2 = 5.640625

Factor a perfect square on the left side:
(p + -0.125)(p + -0.125) = 5.640625

Calculate the square root of the right side: 2.375

Break this problem into two subproblems by setting 
(p + -0.125) equal to 2.375 and -2.375.


Subproblem 1
p + -0.125 = 2.375

Simplifying
p + -0.125 = 2.375

Reorder the terms:
-0.125 + p = 2.375

Solving
-0.125 + p = 2.375

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.125' to each side of the equation.
-0.125 + 0.125 + p = 2.375 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + p = 2.375 + 0.125
p = 2.375 + 0.125

Combine like terms: 2.375 + 0.125 = 2.5
p = 2.5

Simplifying
p = 2.5


Subproblem 2
p + -0.125 = -2.375

Simplifying
p + -0.125 = -2.375

Reorder the terms:
-0.125 + p = -2.375

Solving
-0.125 + p = -2.375

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.125' to each side of the equation.
-0.125 + 0.125 + p = -2.375 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + p = -2.375 + 0.125
p = -2.375 + 0.125

Combine like terms: -2.375 + 0.125 = -2.25
p = -2.25

Simplifying
p = -2.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.5, -2.25}

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