p^2+2p+13=67

Solution for p^2+2p+13=67 equation:

Simplifying
p2 + 2p + 13 = 67

Reorder the terms:
13 + 2p + p2 = 67

Solving
13 + 2p + p2 = 67

Solving for variable 'p'.

Reorder the terms:
13 + -67 + 2p + p2 = 67 + -67

Combine like terms: 13 + -67 = -54
-54 + 2p + p2 = 67 + -67

Combine like terms: 67 + -67 = 0
-54 + 2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 2p + 54 + p2 = 0 + 54

Reorder the terms:
-54 + 54 + 2p + p2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 2p + p2 = 0 + 54
2p + p2 = 0 + 54

Combine like terms: 0 + 54 = 54
2p + p2 = 54

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 = 54 + 1

Reorder the terms:
1 + 2p + p2 = 54 + 1

Combine like terms: 54 + 1 = 55
1 + 2p + p2 = 55

Factor a perfect square on the left side:
(p + 1)(p + 1) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(p + 1) equal to 7.416198487 and -7.416198487.

Subproblem 1
p + 1 = 7.416198487

Simplifying
p + 1 = 7.416198487

Reorder the terms:
1 + p = 7.416198487

Solving
1 + p = 7.416198487

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 = 7.416198487 + -1

Combine like terms: 1 + -1 = 0
0 + p = 7.416198487 + -1
p = 7.416198487 + -1

Combine like terms: 7.416198487 + -1 = 6.416198487
p = 6.416198487

Simplifying
p = 6.416198487

Subproblem 2
p + 1 = -7.416198487

Simplifying
p + 1 = -7.416198487

Reorder the terms:
1 + p = -7.416198487

Solving
1 + p = -7.416198487

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 = -7.416198487 + -1

Combine like terms: 1 + -1 = 0
0 + p = -7.416198487 + -1
p = -7.416198487 + -1

Combine like terms: -7.416198487 + -1 = -8.416198487
p = -8.416198487

Simplifying
p = -8.416198487

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.416198487, -8.416198487}