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 = 87
49 + 14p + p2 = 87

Factor a perfect square on the left side:
(p + 7)(p + 7) = 87

Calculate the square root of the right side: 9.327379053

Break this problem into two subproblems by setting 
(p + 7) equal to 9.327379053 and -9.327379053.


Subproblem 1
p + 7 = 9.327379053

Simplifying
p + 7 = 9.327379053

Reorder the terms:
7 + p = 9.327379053

Solving
7 + p = 9.327379053

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 = 9.327379053 + -7

Combine like terms: 7 + -7 = 0
0 + p = 9.327379053 + -7
p = 9.327379053 + -7

Combine like terms: 9.327379053 + -7 = 2.327379053
p = 2.327379053

Simplifying
p = 2.327379053


Subproblem 2
p + 7 = -9.327379053

Simplifying
p + 7 = -9.327379053

Reorder the terms:
7 + p = -9.327379053

Solving
7 + p = -9.327379053

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 = -9.327379053 + -7

Combine like terms: 7 + -7 = 0
0 + p = -9.327379053 + -7
p = -9.327379053 + -7

Combine like terms: -9.327379053 + -7 = -16.327379053
p = -16.327379053

Simplifying
p = -16.327379053


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.327379053, -16.327379053}

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