r^2+18r-188.4395=0

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Solution for r^2+18r-188.4395=0 equation: 


Simplifying
r2 + 18r + -188.4395 = 0

Reorder the terms:
-188.4395 + 18r + r2 = 0

Solving
-188.4395 + 18r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '188.4395' to each side of the equation.
-188.4395 + 18r + 188.4395 + r2 = 0 + 188.4395

Reorder the terms:
-188.4395 + 188.4395 + 18r + r2 = 0 + 188.4395

Combine like terms: -188.4395 + 188.4395 = 0.0000
0.0000 + 18r + r2 = 0 + 188.4395
18r + r2 = 0 + 188.4395

Combine like terms: 0 + 188.4395 = 188.4395
18r + r2 = 188.4395

The r term is 18r.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18r + 81 + r2 = 188.4395 + 81

Reorder the terms:
81 + 18r + r2 = 188.4395 + 81

Combine like terms: 188.4395 + 81 = 269.4395
81 + 18r + r2 = 269.4395

Factor a perfect square on the left side:
(r + 9)(r + 9) = 269.4395

Calculate the square root of the right side: 16.414612393

Break this problem into two subproblems by setting 
(r + 9) equal to 16.414612393 and -16.414612393.


Subproblem 1
r + 9 = 16.414612393

Simplifying
r + 9 = 16.414612393

Reorder the terms:
9 + r = 16.414612393

Solving
9 + r = 16.414612393

Solving for variable 'r'.

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

Add '-9' to each side of the equation.
9 + -9 + r = 16.414612393 + -9

Combine like terms: 9 + -9 = 0
0 + r = 16.414612393 + -9
r = 16.414612393 + -9

Combine like terms: 16.414612393 + -9 = 7.414612393
r = 7.414612393

Simplifying
r = 7.414612393


Subproblem 2
r + 9 = -16.414612393

Simplifying
r + 9 = -16.414612393

Reorder the terms:
9 + r = -16.414612393

Solving
9 + r = -16.414612393

Solving for variable 'r'.

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

Add '-9' to each side of the equation.
9 + -9 + r = -16.414612393 + -9

Combine like terms: 9 + -9 = 0
0 + r = -16.414612393 + -9
r = -16.414612393 + -9

Combine like terms: -16.414612393 + -9 = -25.414612393
r = -25.414612393

Simplifying
r = -25.414612393


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {7.414612393, -25.414612393}

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