p^2+14p+49=2

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Solution for p^2+14p+49=2 equation: 


Simplifying
p2 + 14p + 49 = 2

Reorder the terms:
49 + 14p + p2 = 2

Solving
49 + 14p + p2 = 2

Solving for variable 'p'.

Reorder the terms:
49 + -2 + 14p + p2 = 2 + -2

Combine like terms: 49 + -2 = 47
47 + 14p + p2 = 2 + -2

Combine like terms: 2 + -2 = 0
47 + 14p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 14p + -47 + p2 = 0 + -47

Reorder the terms:
47 + -47 + 14p + p2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 14p + p2 = 0 + -47
14p + p2 = 0 + -47

Combine like terms: 0 + -47 = -47
14p + p2 = -47

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 = -47 + 49

Reorder the terms:
49 + 14p + p2 = -47 + 49

Combine like terms: -47 + 49 = 2
49 + 14p + p2 = 2

Factor a perfect square on the left side:
(p + 7)(p + 7) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(p + 7) equal to 1.414213562 and -1.414213562.


Subproblem 1
p + 7 = 1.414213562

Simplifying
p + 7 = 1.414213562

Reorder the terms:
7 + p = 1.414213562

Solving
7 + p = 1.414213562

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 = 1.414213562 + -7

Combine like terms: 7 + -7 = 0
0 + p = 1.414213562 + -7
p = 1.414213562 + -7

Combine like terms: 1.414213562 + -7 = -5.585786438
p = -5.585786438

Simplifying
p = -5.585786438


Subproblem 2
p + 7 = -1.414213562

Simplifying
p + 7 = -1.414213562

Reorder the terms:
7 + p = -1.414213562

Solving
7 + p = -1.414213562

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 = -1.414213562 + -7

Combine like terms: 7 + -7 = 0
0 + p = -1.414213562 + -7
p = -1.414213562 + -7

Combine like terms: -1.414213562 + -7 = -8.414213562
p = -8.414213562

Simplifying
p = -8.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-5.585786438, -8.414213562}

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