p^2-6p+7=0

Solution for p^2-6p+7=0 equation:

Simplifying
p2 + -6p + 7 = 0

Reorder the terms:
7 + -6p + p2 = 0

Solving
7 + -6p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6p + -7 + p2 = 0 + -7

Reorder the terms:
7 + -7 + -6p + p2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6p + p2 = 0 + -7
-6p + p2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6p + p2 = -7

The p term is -6p.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6p + 9 + p2 = -7 + 9

Reorder the terms:
9 + -6p + p2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + -6p + p2 = 2

Factor a perfect square on the left side:
(p + -3)(p + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(p + -3) equal to 1.414213562 and -1.414213562.

Subproblem 1
p + -3 = 1.414213562

Simplifying
p + -3 = 1.414213562

Reorder the terms:
-3 + p = 1.414213562

Solving
-3 + p = 1.414213562

Solving for variable 'p'.

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

Add '3' to each side of the equation.
-3 + 3 + p = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + p = 1.414213562 + 3
p = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
p = 4.414213562

Simplifying
p = 4.414213562

Subproblem 2
p + -3 = -1.414213562

Simplifying
p + -3 = -1.414213562

Reorder the terms:
-3 + p = -1.414213562

Solving
-3 + p = -1.414213562

Solving for variable 'p'.

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

Add '3' to each side of the equation.
-3 + 3 + p = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + p = -1.414213562 + 3
p = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
p = 1.585786438

Simplifying
p = 1.585786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.414213562, 1.585786438}