4p^2+40p+52=0

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Solution for 4p^2+40p+52=0 equation: 


Simplifying
4p2 + 40p + 52 = 0

Reorder the terms:
52 + 40p + 4p2 = 0

Solving
52 + 40p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(13 + 10p + p2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(13 + 10p + p2)' equal to zero and attempt to solve:

Simplifying
13 + 10p + p2 = 0

Solving
13 + 10p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 10p + -13 + p2 = 0 + -13

Reorder the terms:
13 + -13 + 10p + p2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 10p + p2 = 0 + -13
10p + p2 = 0 + -13

Combine like terms: 0 + -13 = -13
10p + p2 = -13

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 = -13 + 25

Reorder the terms:
25 + 10p + p2 = -13 + 25

Combine like terms: -13 + 25 = 12
25 + 10p + p2 = 12

Factor a perfect square on the left side:
(p + 5)(p + 5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(p + 5) equal to 3.464101615 and -3.464101615.


Subproblem 1
p + 5 = 3.464101615

Simplifying
p + 5 = 3.464101615

Reorder the terms:
5 + p = 3.464101615

Solving
5 + p = 3.464101615

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 = 3.464101615 + -5

Combine like terms: 5 + -5 = 0
0 + p = 3.464101615 + -5
p = 3.464101615 + -5

Combine like terms: 3.464101615 + -5 = -1.535898385
p = -1.535898385

Simplifying
p = -1.535898385


Subproblem 2
p + 5 = -3.464101615

Simplifying
p + 5 = -3.464101615

Reorder the terms:
5 + p = -3.464101615

Solving
5 + p = -3.464101615

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 = -3.464101615 + -5

Combine like terms: 5 + -5 = 0
0 + p = -3.464101615 + -5
p = -3.464101615 + -5

Combine like terms: -3.464101615 + -5 = -8.464101615
p = -8.464101615

Simplifying
p = -8.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-1.535898385, -8.464101615}
Solution
p = {-1.535898385, -8.464101615}

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