(p+7)(p+7)=13

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Solution for (p+7)(p+7)=13 equation:


Simplifying
(p + 7)(p + 7) = 13

Reorder the terms:
(7 + p)(p + 7) = 13

Reorder the terms:
(7 + p)(7 + p) = 13

Multiply (7 + p) * (7 + p)
(7(7 + p) + p(7 + p)) = 13
((7 * 7 + p * 7) + p(7 + p)) = 13
((49 + 7p) + p(7 + p)) = 13
(49 + 7p + (7 * p + p * p)) = 13
(49 + 7p + (7p + p2)) = 13

Combine like terms: 7p + 7p = 14p
(49 + 14p + p2) = 13

Solving
49 + 14p + p2 = 13

Solving for variable 'p'.

Reorder the terms:
49 + -13 + 14p + p2 = 13 + -13

Combine like terms: 49 + -13 = 36
36 + 14p + p2 = 13 + -13

Combine like terms: 13 + -13 = 0
36 + 14p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 14p + -36 + p2 = 0 + -36

Reorder the terms:
36 + -36 + 14p + p2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 14p + p2 = 0 + -36
14p + p2 = 0 + -36

Combine like terms: 0 + -36 = -36
14p + p2 = -36

The p term is 14p.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14p + 49 + p2 = -36 + 49

Reorder the terms:
49 + 14p + p2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + 14p + p2 = 13

Factor a perfect square on the left side:
(p + 7)(p + 7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(p + 7) equal to 3.605551275 and -3.605551275.


Subproblem 1
p + 7 = 3.605551275

Simplifying
p + 7 = 3.605551275

Reorder the terms:
7 + p = 3.605551275

Solving
7 + p = 3.605551275

Solving for variable 'p'.

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

Add '-7' to each side of the equation.
7 + -7 + p = 3.605551275 + -7

Combine like terms: 7 + -7 = 0
0 + p = 3.605551275 + -7
p = 3.605551275 + -7

Combine like terms: 3.605551275 + -7 = -3.394448725
p = -3.394448725

Simplifying
p = -3.394448725


Subproblem 2
p + 7 = -3.605551275

Simplifying
p + 7 = -3.605551275

Reorder the terms:
7 + p = -3.605551275

Solving
7 + p = -3.605551275

Solving for variable 'p'.

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

Add '-7' to each side of the equation.
7 + -7 + p = -3.605551275 + -7

Combine like terms: 7 + -7 = 0
0 + p = -3.605551275 + -7
p = -3.605551275 + -7

Combine like terms: -3.605551275 + -7 = -10.605551275
p = -10.605551275

Simplifying
p = -10.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-3.394448725, -10.605551275}

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