p^2-14p-18=0

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Solution for p^2-14p-18=0 equation: 


Simplifying
p2 + -14p + -18 = 0

Reorder the terms:
-18 + -14p + p2 = 0

Solving
-18 + -14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -14p + 18 + p2 = 0 + 18

Reorder the terms:
-18 + 18 + -14p + p2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -14p + p2 = 0 + 18
-14p + p2 = 0 + 18

Combine like terms: 0 + 18 = 18
-14p + p2 = 18

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 = 18 + 49

Reorder the terms:
49 + -14p + p2 = 18 + 49

Combine like terms: 18 + 49 = 67
49 + -14p + p2 = 67

Factor a perfect square on the left side:
(p + -7)(p + -7) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(p + -7) equal to 8.185352772 and -8.185352772.


Subproblem 1
p + -7 = 8.185352772

Simplifying
p + -7 = 8.185352772

Reorder the terms:
-7 + p = 8.185352772

Solving
-7 + p = 8.185352772

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 = 8.185352772 + 7

Combine like terms: -7 + 7 = 0
0 + p = 8.185352772 + 7
p = 8.185352772 + 7

Combine like terms: 8.185352772 + 7 = 15.185352772
p = 15.185352772

Simplifying
p = 15.185352772


Subproblem 2
p + -7 = -8.185352772

Simplifying
p + -7 = -8.185352772

Reorder the terms:
-7 + p = -8.185352772

Solving
-7 + p = -8.185352772

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 = -8.185352772 + 7

Combine like terms: -7 + 7 = 0
0 + p = -8.185352772 + 7
p = -8.185352772 + 7

Combine like terms: -8.185352772 + 7 = -1.185352772
p = -1.185352772

Simplifying
p = -1.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {15.185352772, -1.185352772}

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