6r^2-11r-56=0

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Solution for 6r^2-11r-56=0 equation: 


Simplifying
6r2 + -11r + -56 = 0

Reorder the terms:
-56 + -11r + 6r2 = 0

Solving
-56 + -11r + 6r2 = 0

Solving for variable 'r'.

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

Divide each side by '6'.
-9.333333333 + -1.833333333r + r2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + -1.833333333r + 9.333333333 + r2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + -1.833333333r + r2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + -1.833333333r + r2 = 0 + 9.333333333
-1.833333333r + r2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
-1.833333333r + r2 = 9.333333333

The r term is -1.833333333r.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333r + 0.8402777775 + r2 = 9.333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333r + r2 = 9.333333333 + 0.8402777775

Combine like terms: 9.333333333 + 0.8402777775 = 10.1736111105
0.8402777775 + -1.833333333r + r2 = 10.1736111105

Factor a perfect square on the left side:
(r + -0.9166666665)(r + -0.9166666665) = 10.1736111105

Calculate the square root of the right side: 3.189609868

Break this problem into two subproblems by setting 
(r + -0.9166666665) equal to 3.189609868 and -3.189609868.


Subproblem 1
r + -0.9166666665 = 3.189609868

Simplifying
r + -0.9166666665 = 3.189609868

Reorder the terms:
-0.9166666665 + r = 3.189609868

Solving
-0.9166666665 + r = 3.189609868

Solving for variable 'r'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + r = 3.189609868 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + r = 3.189609868 + 0.9166666665
r = 3.189609868 + 0.9166666665

Combine like terms: 3.189609868 + 0.9166666665 = 4.1062765345
r = 4.1062765345

Simplifying
r = 4.1062765345


Subproblem 2
r + -0.9166666665 = -3.189609868

Simplifying
r + -0.9166666665 = -3.189609868

Reorder the terms:
-0.9166666665 + r = -3.189609868

Solving
-0.9166666665 + r = -3.189609868

Solving for variable 'r'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + r = -3.189609868 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + r = -3.189609868 + 0.9166666665
r = -3.189609868 + 0.9166666665

Combine like terms: -3.189609868 + 0.9166666665 = -2.2729432015
r = -2.2729432015

Simplifying
r = -2.2729432015


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.1062765345, -2.2729432015}

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