4p^2-40p+56=0

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Solution for 4p^2-40p+56=0 equation: 


Simplifying
4p2 + -40p + 56 = 0

Reorder the terms:
56 + -40p + 4p2 = 0

Solving
56 + -40p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + -10p + p2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(14 + -10p + p2)' equal to zero and attempt to solve:

Simplifying
14 + -10p + p2 = 0

Solving
14 + -10p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -10p + -14 + p2 = 0 + -14

Reorder the terms:
14 + -14 + -10p + p2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -10p + p2 = 0 + -14
-10p + p2 = 0 + -14

Combine like terms: 0 + -14 = -14
-10p + p2 = -14

The p term is -10p.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10p + 25 + p2 = -14 + 25

Reorder the terms:
25 + -10p + p2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + -10p + p2 = 11

Factor a perfect square on the left side:
(p + -5)(p + -5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(p + -5) equal to 3.31662479 and -3.31662479.


Subproblem 1
p + -5 = 3.31662479

Simplifying
p + -5 = 3.31662479

Reorder the terms:
-5 + p = 3.31662479

Solving
-5 + p = 3.31662479

Solving for variable 'p'.

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

Add '5' to each side of the equation.
-5 + 5 + p = 3.31662479 + 5

Combine like terms: -5 + 5 = 0
0 + p = 3.31662479 + 5
p = 3.31662479 + 5

Combine like terms: 3.31662479 + 5 = 8.31662479
p = 8.31662479

Simplifying
p = 8.31662479


Subproblem 2
p + -5 = -3.31662479

Simplifying
p + -5 = -3.31662479

Reorder the terms:
-5 + p = -3.31662479

Solving
-5 + p = -3.31662479

Solving for variable 'p'.

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

Add '5' to each side of the equation.
-5 + 5 + p = -3.31662479 + 5

Combine like terms: -5 + 5 = 0
0 + p = -3.31662479 + 5
p = -3.31662479 + 5

Combine like terms: -3.31662479 + 5 = 1.68337521
p = 1.68337521

Simplifying
p = 1.68337521


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {8.31662479, 1.68337521}
Solution
p = {8.31662479, 1.68337521}

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