p^2-12p+14=0

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

Simplifying
p2 + -12p + 14 = 0

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

Solving
14 + -12p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The p term is -12p.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12p + 36 + p2 = -14 + 36

Reorder the terms:
36 + -12p + p2 = -14 + 36

Combine like terms: -14 + 36 = 22
36 + -12p + p2 = 22

Factor a perfect square on the left side:
(p + -6)(p + -6) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(p + -6) equal to 4.69041576 and -4.69041576.

Subproblem 1
p + -6 = 4.69041576

Simplifying
p + -6 = 4.69041576

Reorder the terms:
-6 + p = 4.69041576

Solving
-6 + p = 4.69041576

Solving for variable 'p'.

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

Add '6' to each side of the equation.
-6 + 6 + p = 4.69041576 + 6

Combine like terms: -6 + 6 = 0
0 + p = 4.69041576 + 6
p = 4.69041576 + 6

Combine like terms: 4.69041576 + 6 = 10.69041576
p = 10.69041576

Simplifying
p = 10.69041576

Subproblem 2
p + -6 = -4.69041576

Simplifying
p + -6 = -4.69041576

Reorder the terms:
-6 + p = -4.69041576

Solving
-6 + p = -4.69041576

Solving for variable 'p'.

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

Add '6' to each side of the equation.
-6 + 6 + p = -4.69041576 + 6

Combine like terms: -6 + 6 = 0
0 + p = -4.69041576 + 6
p = -4.69041576 + 6

Combine like terms: -4.69041576 + 6 = 1.30958424
p = 1.30958424

Simplifying
p = 1.30958424

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {10.69041576, 1.30958424}