p^2-14p+12=0

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Solution for p^2-14p+12=0 equation: 


Simplifying
p2 + -14p + 12 = 0

Reorder the terms:
12 + -14p + p2 = 0

Solving
12 + -14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -14p + -12 + p2 = 0 + -12

Reorder the terms:
12 + -12 + -14p + p2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -14p + p2 = 0 + -12
-14p + p2 = 0 + -12

Combine like terms: 0 + -12 = -12
-14p + p2 = -12

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 = -12 + 49

Reorder the terms:
49 + -14p + p2 = -12 + 49

Combine like terms: -12 + 49 = 37
49 + -14p + p2 = 37

Factor a perfect square on the left side:
(p + -7)(p + -7) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(p + -7) equal to 6.08276253 and -6.08276253.


Subproblem 1
p + -7 = 6.08276253

Simplifying
p + -7 = 6.08276253

Reorder the terms:
-7 + p = 6.08276253

Solving
-7 + p = 6.08276253

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 = 6.08276253 + 7

Combine like terms: -7 + 7 = 0
0 + p = 6.08276253 + 7
p = 6.08276253 + 7

Combine like terms: 6.08276253 + 7 = 13.08276253
p = 13.08276253

Simplifying
p = 13.08276253


Subproblem 2
p + -7 = -6.08276253

Simplifying
p + -7 = -6.08276253

Reorder the terms:
-7 + p = -6.08276253

Solving
-7 + p = -6.08276253

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 = -6.08276253 + 7

Combine like terms: -7 + 7 = 0
0 + p = -6.08276253 + 7
p = -6.08276253 + 7

Combine like terms: -6.08276253 + 7 = 0.91723747
p = 0.91723747

Simplifying
p = 0.91723747


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {13.08276253, 0.91723747}

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