3r^2+66r=-111

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Solution for 3r^2+66r=-111 equation: 


Simplifying
3r2 + 66r = -111

Reorder the terms:
66r + 3r2 = -111

Solving
66r + 3r2 = -111

Solving for variable 'r'.

Reorder the terms:
111 + 66r + 3r2 = -111 + 111

Combine like terms: -111 + 111 = 0
111 + 66r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(37 + 22r + r2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(37 + 22r + r2)' equal to zero and attempt to solve:

Simplifying
37 + 22r + r2 = 0

Solving
37 + 22r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + 22r + -37 + r2 = 0 + -37

Reorder the terms:
37 + -37 + 22r + r2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 22r + r2 = 0 + -37
22r + r2 = 0 + -37

Combine like terms: 0 + -37 = -37
22r + r2 = -37

The r term is 22r.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22r + 121 + r2 = -37 + 121

Reorder the terms:
121 + 22r + r2 = -37 + 121

Combine like terms: -37 + 121 = 84
121 + 22r + r2 = 84

Factor a perfect square on the left side:
(r + 11)(r + 11) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(r + 11) equal to 9.16515139 and -9.16515139.


Subproblem 1
r + 11 = 9.16515139

Simplifying
r + 11 = 9.16515139

Reorder the terms:
11 + r = 9.16515139

Solving
11 + r = 9.16515139

Solving for variable 'r'.

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

Add '-11' to each side of the equation.
11 + -11 + r = 9.16515139 + -11

Combine like terms: 11 + -11 = 0
0 + r = 9.16515139 + -11
r = 9.16515139 + -11

Combine like terms: 9.16515139 + -11 = -1.83484861
r = -1.83484861

Simplifying
r = -1.83484861


Subproblem 2
r + 11 = -9.16515139

Simplifying
r + 11 = -9.16515139

Reorder the terms:
11 + r = -9.16515139

Solving
11 + r = -9.16515139

Solving for variable 'r'.

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

Add '-11' to each side of the equation.
11 + -11 + r = -9.16515139 + -11

Combine like terms: 11 + -11 = 0
0 + r = -9.16515139 + -11
r = -9.16515139 + -11

Combine like terms: -9.16515139 + -11 = -20.16515139
r = -20.16515139

Simplifying
r = -20.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-1.83484861, -20.16515139}
Solution
r = {-1.83484861, -20.16515139}

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