p^2+18+81p=0

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Solution for p^2+18+81p=0 equation: 


Simplifying
p2 + 18 + 81p = 0

Reorder the terms:
18 + 81p + p2 = 0

Solving
18 + 81p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 81p + -18 + p2 = 0 + -18

Reorder the terms:
18 + -18 + 81p + p2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 81p + p2 = 0 + -18
81p + p2 = 0 + -18

Combine like terms: 0 + -18 = -18
81p + p2 = -18

The p term is 81p.  Take half its coefficient (40.5).
Square it (1640.25) and add it to both sides.

Add '1640.25' to each side of the equation.
81p + 1640.25 + p2 = -18 + 1640.25

Reorder the terms:
1640.25 + 81p + p2 = -18 + 1640.25

Combine like terms: -18 + 1640.25 = 1622.25
1640.25 + 81p + p2 = 1622.25

Factor a perfect square on the left side:
(p + 40.5)(p + 40.5) = 1622.25

Calculate the square root of the right side: 40.277164746

Break this problem into two subproblems by setting 
(p + 40.5) equal to 40.277164746 and -40.277164746.


Subproblem 1
p + 40.5 = 40.277164746

Simplifying
p + 40.5 = 40.277164746

Reorder the terms:
40.5 + p = 40.277164746

Solving
40.5 + p = 40.277164746

Solving for variable 'p'.

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

Add '-40.5' to each side of the equation.
40.5 + -40.5 + p = 40.277164746 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + p = 40.277164746 + -40.5
p = 40.277164746 + -40.5

Combine like terms: 40.277164746 + -40.5 = -0.222835254
p = -0.222835254

Simplifying
p = -0.222835254


Subproblem 2
p + 40.5 = -40.277164746

Simplifying
p + 40.5 = -40.277164746

Reorder the terms:
40.5 + p = -40.277164746

Solving
40.5 + p = -40.277164746

Solving for variable 'p'.

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

Add '-40.5' to each side of the equation.
40.5 + -40.5 + p = -40.277164746 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + p = -40.277164746 + -40.5
p = -40.277164746 + -40.5

Combine like terms: -40.277164746 + -40.5 = -80.777164746
p = -80.777164746

Simplifying
p = -80.777164746


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.222835254, -80.777164746}

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