12r^2+11r=20

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Solution for 12r^2+11r=20 equation: 


Simplifying
12r2 + 11r = 20

Reorder the terms:
11r + 12r2 = 20

Solving
11r + 12r2 = 20

Solving for variable 'r'.

Reorder the terms:
-20 + 11r + 12r2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 11r + 12r2 = 0

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
-1.666666667 + 0.9166666667r + r2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.9166666667r + 1.666666667 + r2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.9166666667r + r2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.9166666667r + r2 = 0 + 1.666666667
0.9166666667r + r2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.9166666667r + r2 = 1.666666667

The r term is 0.9166666667r.  Take half its coefficient (0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
0.9166666667r + 0.2100694445 + r2 = 1.666666667 + 0.2100694445

Reorder the terms:
0.2100694445 + 0.9166666667r + r2 = 1.666666667 + 0.2100694445

Combine like terms: 1.666666667 + 0.2100694445 = 1.8767361115
0.2100694445 + 0.9166666667r + r2 = 1.8767361115

Factor a perfect square on the left side:
(r + 0.4583333334)(r + 0.4583333334) = 1.8767361115

Calculate the square root of the right side: 1.369940185

Break this problem into two subproblems by setting 
(r + 0.4583333334) equal to 1.369940185 and -1.369940185.


Subproblem 1
r + 0.4583333334 = 1.369940185

Simplifying
r + 0.4583333334 = 1.369940185

Reorder the terms:
0.4583333334 + r = 1.369940185

Solving
0.4583333334 + r = 1.369940185

Solving for variable 'r'.

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

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + r = 1.369940185 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + r = 1.369940185 + -0.4583333334
r = 1.369940185 + -0.4583333334

Combine like terms: 1.369940185 + -0.4583333334 = 0.9116068516
r = 0.9116068516

Simplifying
r = 0.9116068516


Subproblem 2
r + 0.4583333334 = -1.369940185

Simplifying
r + 0.4583333334 = -1.369940185

Reorder the terms:
0.4583333334 + r = -1.369940185

Solving
0.4583333334 + r = -1.369940185

Solving for variable 'r'.

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

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + r = -1.369940185 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + r = -1.369940185 + -0.4583333334
r = -1.369940185 + -0.4583333334

Combine like terms: -1.369940185 + -0.4583333334 = -1.8282735184
r = -1.8282735184

Simplifying
r = -1.8282735184


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.9116068516, -1.8282735184}

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