p^2+14p-3=0

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Solution for p^2+14p-3=0 equation: 


Simplifying
p2 + 14p + -3 = 0

Reorder the terms:
-3 + 14p + p2 = 0

Solving
-3 + 14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 14p + 3 + p2 = 0 + 3

Reorder the terms:
-3 + 3 + 14p + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 14p + p2 = 0 + 3
14p + p2 = 0 + 3

Combine like terms: 0 + 3 = 3
14p + p2 = 3

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 = 3 + 49

Reorder the terms:
49 + 14p + p2 = 3 + 49

Combine like terms: 3 + 49 = 52
49 + 14p + p2 = 52

Factor a perfect square on the left side:
(p + 7)(p + 7) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(p + 7) equal to 7.211102551 and -7.211102551.


Subproblem 1
p + 7 = 7.211102551

Simplifying
p + 7 = 7.211102551

Reorder the terms:
7 + p = 7.211102551

Solving
7 + p = 7.211102551

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 = 7.211102551 + -7

Combine like terms: 7 + -7 = 0
0 + p = 7.211102551 + -7
p = 7.211102551 + -7

Combine like terms: 7.211102551 + -7 = 0.211102551
p = 0.211102551

Simplifying
p = 0.211102551


Subproblem 2
p + 7 = -7.211102551

Simplifying
p + 7 = -7.211102551

Reorder the terms:
7 + p = -7.211102551

Solving
7 + p = -7.211102551

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 = -7.211102551 + -7

Combine like terms: 7 + -7 = 0
0 + p = -7.211102551 + -7
p = -7.211102551 + -7

Combine like terms: -7.211102551 + -7 = -14.211102551
p = -14.211102551

Simplifying
p = -14.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.211102551, -14.211102551}

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