r^2+18r+14=0

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Solution for r^2+18r+14=0 equation: 


Simplifying
r2 + 18r + 14 = 0

Reorder the terms:
14 + 18r + r2 = 0

Solving
14 + 18r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 18r + -14 + r2 = 0 + -14

Reorder the terms:
14 + -14 + 18r + r2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 18r + r2 = 0 + -14
18r + r2 = 0 + -14

Combine like terms: 0 + -14 = -14
18r + r2 = -14

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 = -14 + 81

Reorder the terms:
81 + 18r + r2 = -14 + 81

Combine like terms: -14 + 81 = 67
81 + 18r + r2 = 67

Factor a perfect square on the left side:
(r + 9)(r + 9) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(r + 9) equal to 8.185352772 and -8.185352772.


Subproblem 1
r + 9 = 8.185352772

Simplifying
r + 9 = 8.185352772

Reorder the terms:
9 + r = 8.185352772

Solving
9 + r = 8.185352772

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 = 8.185352772 + -9

Combine like terms: 9 + -9 = 0
0 + r = 8.185352772 + -9
r = 8.185352772 + -9

Combine like terms: 8.185352772 + -9 = -0.814647228
r = -0.814647228

Simplifying
r = -0.814647228


Subproblem 2
r + 9 = -8.185352772

Simplifying
r + 9 = -8.185352772

Reorder the terms:
9 + r = -8.185352772

Solving
9 + r = -8.185352772

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 = -8.185352772 + -9

Combine like terms: 9 + -9 = 0
0 + r = -8.185352772 + -9
r = -8.185352772 + -9

Combine like terms: -8.185352772 + -9 = -17.185352772
r = -17.185352772

Simplifying
r = -17.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.814647228, -17.185352772}

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