r^2+11r-18=0

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Solution for r^2+11r-18=0 equation: 


Simplifying
r2 + 11r + -18 = 0

Reorder the terms:
-18 + 11r + r2 = 0

Solving
-18 + 11r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 11r + 18 + r2 = 0 + 18

Reorder the terms:
-18 + 18 + 11r + r2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 11r + r2 = 0 + 18
11r + r2 = 0 + 18

Combine like terms: 0 + 18 = 18
11r + r2 = 18

The r term is 11r.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11r + 30.25 + r2 = 18 + 30.25

Reorder the terms:
30.25 + 11r + r2 = 18 + 30.25

Combine like terms: 18 + 30.25 = 48.25
30.25 + 11r + r2 = 48.25

Factor a perfect square on the left side:
(r + 5.5)(r + 5.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(r + 5.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
r + 5.5 = 6.946221995

Simplifying
r + 5.5 = 6.946221995

Reorder the terms:
5.5 + r = 6.946221995

Solving
5.5 + r = 6.946221995

Solving for variable 'r'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + r = 6.946221995 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + r = 6.946221995 + -5.5
r = 6.946221995 + -5.5

Combine like terms: 6.946221995 + -5.5 = 1.446221995
r = 1.446221995

Simplifying
r = 1.446221995


Subproblem 2
r + 5.5 = -6.946221995

Simplifying
r + 5.5 = -6.946221995

Reorder the terms:
5.5 + r = -6.946221995

Solving
5.5 + r = -6.946221995

Solving for variable 'r'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + r = -6.946221995 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + r = -6.946221995 + -5.5
r = -6.946221995 + -5.5

Combine like terms: -6.946221995 + -5.5 = -12.446221995
r = -12.446221995

Simplifying
r = -12.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.446221995, -12.446221995}

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