-32p^2+48p-4=0

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Solution for -32p^2+48p-4=0 equation: 


Simplifying
-32p2 + 48p + -4 = 0

Reorder the terms:
-4 + 48p + -32p2 = 0

Solving
-4 + 48p + -32p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 12p + -8p2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 12p + -8p2)' equal to zero and attempt to solve:

Simplifying
-1 + 12p + -8p2 = 0

Solving
-1 + 12p + -8p2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.125 + -1.5p + p2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1.5p + -0.125 + p2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1.5p + p2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1.5p + p2 = 0 + -0.125
-1.5p + p2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1.5p + p2 = -0.125

The p term is -1.5p.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5p + 0.5625 + p2 = -0.125 + 0.5625

Reorder the terms:
0.5625 + -1.5p + p2 = -0.125 + 0.5625

Combine like terms: -0.125 + 0.5625 = 0.4375
0.5625 + -1.5p + p2 = 0.4375

Factor a perfect square on the left side:
(p + -0.75)(p + -0.75) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(p + -0.75) equal to 0.661437828 and -0.661437828.


Subproblem 1
p + -0.75 = 0.661437828

Simplifying
p + -0.75 = 0.661437828

Reorder the terms:
-0.75 + p = 0.661437828

Solving
-0.75 + p = 0.661437828

Solving for variable 'p'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + p = 0.661437828 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + p = 0.661437828 + 0.75
p = 0.661437828 + 0.75

Combine like terms: 0.661437828 + 0.75 = 1.411437828
p = 1.411437828

Simplifying
p = 1.411437828


Subproblem 2
p + -0.75 = -0.661437828

Simplifying
p + -0.75 = -0.661437828

Reorder the terms:
-0.75 + p = -0.661437828

Solving
-0.75 + p = -0.661437828

Solving for variable 'p'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + p = -0.661437828 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + p = -0.661437828 + 0.75
p = -0.661437828 + 0.75

Combine like terms: -0.661437828 + 0.75 = 0.088562172
p = 0.088562172

Simplifying
p = 0.088562172


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.411437828, 0.088562172}
Solution
p = {1.411437828, 0.088562172}

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