p^2+14p+38=0

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Solution for p^2+14p+38=0 equation: 


Simplifying
p2 + 14p + 38 = 0

Reorder the terms:
38 + 14p + p2 = 0

Solving
38 + 14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-38' to each side of the equation.
38 + 14p + -38 + p2 = 0 + -38

Reorder the terms:
38 + -38 + 14p + p2 = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 14p + p2 = 0 + -38
14p + p2 = 0 + -38

Combine like terms: 0 + -38 = -38
14p + p2 = -38

The p term is 14p.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14p + 49 + p2 = -38 + 49

Reorder the terms:
49 + 14p + p2 = -38 + 49

Combine like terms: -38 + 49 = 11
49 + 14p + p2 = 11

Factor a perfect square on the left side:
(p + 7)(p + 7) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(p + 7) equal to 3.31662479 and -3.31662479.


Subproblem 1
p + 7 = 3.31662479

Simplifying
p + 7 = 3.31662479

Reorder the terms:
7 + p = 3.31662479

Solving
7 + p = 3.31662479

Solving for variable 'p'.

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

Add '-7' to each side of the equation.
7 + -7 + p = 3.31662479 + -7

Combine like terms: 7 + -7 = 0
0 + p = 3.31662479 + -7
p = 3.31662479 + -7

Combine like terms: 3.31662479 + -7 = -3.68337521
p = -3.68337521

Simplifying
p = -3.68337521


Subproblem 2
p + 7 = -3.31662479

Simplifying
p + 7 = -3.31662479

Reorder the terms:
7 + p = -3.31662479

Solving
7 + p = -3.31662479

Solving for variable 'p'.

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

Add '-7' to each side of the equation.
7 + -7 + p = -3.31662479 + -7

Combine like terms: 7 + -7 = 0
0 + p = -3.31662479 + -7
p = -3.31662479 + -7

Combine like terms: -3.31662479 + -7 = -10.31662479
p = -10.31662479

Simplifying
p = -10.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-3.68337521, -10.31662479}

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