p^2-2p+6=55

Solution for p^2-2p+6=55 equation:

Simplifying
p2 + -2p + 6 = 55

Reorder the terms:
6 + -2p + p2 = 55

Solving
6 + -2p + p2 = 55

Solving for variable 'p'.

Reorder the terms:
6 + -55 + -2p + p2 = 55 + -55

Combine like terms: 6 + -55 = -49
-49 + -2p + p2 = 55 + -55

Combine like terms: 55 + -55 = 0
-49 + -2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -2p + 49 + p2 = 0 + 49

Reorder the terms:
-49 + 49 + -2p + p2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -2p + p2 = 0 + 49
-2p + p2 = 0 + 49

Combine like terms: 0 + 49 = 49
-2p + p2 = 49

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = 49 + 1

Reorder the terms:
1 + -2p + p2 = 49 + 1

Combine like terms: 49 + 1 = 50
1 + -2p + p2 = 50

Factor a perfect square on the left side:
(p + -1)(p + -1) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(p + -1) equal to 7.071067812 and -7.071067812.

Subproblem 1
p + -1 = 7.071067812

Simplifying
p + -1 = 7.071067812

Reorder the terms:
-1 + p = 7.071067812

Solving
-1 + p = 7.071067812

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + p = 7.071067812 + 1
p = 7.071067812 + 1

Combine like terms: 7.071067812 + 1 = 8.071067812
p = 8.071067812

Simplifying
p = 8.071067812

Subproblem 2
p + -1 = -7.071067812

Simplifying
p + -1 = -7.071067812

Reorder the terms:
-1 + p = -7.071067812

Solving
-1 + p = -7.071067812

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + p = -7.071067812 + 1
p = -7.071067812 + 1

Combine like terms: -7.071067812 + 1 = -6.071067812
p = -6.071067812

Simplifying
p = -6.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {8.071067812, -6.071067812}