p^2+26p+7=0

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Solution for p^2+26p+7=0 equation: 


Simplifying
p2 + 26p + 7 = 0

Reorder the terms:
7 + 26p + p2 = 0

Solving
7 + 26p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 26p + -7 + p2 = 0 + -7

Reorder the terms:
7 + -7 + 26p + p2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 26p + p2 = 0 + -7
26p + p2 = 0 + -7

Combine like terms: 0 + -7 = -7
26p + p2 = -7

The p term is 26p.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26p + 169 + p2 = -7 + 169

Reorder the terms:
169 + 26p + p2 = -7 + 169

Combine like terms: -7 + 169 = 162
169 + 26p + p2 = 162

Factor a perfect square on the left side:
(p + 13)(p + 13) = 162

Calculate the square root of the right side: 12.727922061

Break this problem into two subproblems by setting 
(p + 13) equal to 12.727922061 and -12.727922061.


Subproblem 1
p + 13 = 12.727922061

Simplifying
p + 13 = 12.727922061

Reorder the terms:
13 + p = 12.727922061

Solving
13 + p = 12.727922061

Solving for variable 'p'.

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

Add '-13' to each side of the equation.
13 + -13 + p = 12.727922061 + -13

Combine like terms: 13 + -13 = 0
0 + p = 12.727922061 + -13
p = 12.727922061 + -13

Combine like terms: 12.727922061 + -13 = -0.272077939
p = -0.272077939

Simplifying
p = -0.272077939


Subproblem 2
p + 13 = -12.727922061

Simplifying
p + 13 = -12.727922061

Reorder the terms:
13 + p = -12.727922061

Solving
13 + p = -12.727922061

Solving for variable 'p'.

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

Add '-13' to each side of the equation.
13 + -13 + p = -12.727922061 + -13

Combine like terms: 13 + -13 = 0
0 + p = -12.727922061 + -13
p = -12.727922061 + -13

Combine like terms: -12.727922061 + -13 = -25.727922061
p = -25.727922061

Simplifying
p = -25.727922061


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.272077939, -25.727922061}

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