p^2+2p+1=6

Solution for p^2+2p+1=6 equation:

Simplifying
p2 + 2p + 1 = 6

Reorder the terms:
1 + 2p + p2 = 6

Solving
1 + 2p + p2 = 6

Solving for variable 'p'.

Reorder the terms:
1 + -6 + 2p + p2 = 6 + -6

Combine like terms: 1 + -6 = -5
-5 + 2p + p2 = 6 + -6

Combine like terms: 6 + -6 = 0
-5 + 2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2p + 5 + p2 = 0 + 5

Reorder the terms:
-5 + 5 + 2p + p2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2p + p2 = 0 + 5
2p + p2 = 0 + 5

Combine like terms: 0 + 5 = 5
2p + p2 = 5

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 = 5 + 1

Reorder the terms:
1 + 2p + p2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2p + p2 = 6

Factor a perfect square on the left side:
(p + 1)(p + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(p + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1
p + 1 = 2.449489743

Simplifying
p + 1 = 2.449489743

Reorder the terms:
1 + p = 2.449489743

Solving
1 + p = 2.449489743

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 = 2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + p = 2.449489743 + -1
p = 2.449489743 + -1

Combine like terms: 2.449489743 + -1 = 1.449489743
p = 1.449489743

Simplifying
p = 1.449489743

Subproblem 2
p + 1 = -2.449489743

Simplifying
p + 1 = -2.449489743

Reorder the terms:
1 + p = -2.449489743

Solving
1 + p = -2.449489743

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 = -2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + p = -2.449489743 + -1
p = -2.449489743 + -1

Combine like terms: -2.449489743 + -1 = -3.449489743
p = -3.449489743

Simplifying
p = -3.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.449489743, -3.449489743}