r-6r^2=-11

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


Simplifying
r + -6r2 = -11

Solving
r + -6r2 = -11

Solving for variable 'r'.

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

Combine like terms: -11 + 11 = 0
11 + r + -6r2 = 0

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

Divide each side by '-6'.
-1.833333333 + -0.1666666667r + r2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + -0.1666666667r + 1.833333333 + r2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + -0.1666666667r + r2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + -0.1666666667r + r2 = 0 + 1.833333333
-0.1666666667r + r2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
-0.1666666667r + r2 = 1.833333333

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.1666666667r + 0.25 + r2 = 1.833333333 + 0.25

Reorder the terms:
0.25 + -0.1666666667r + r2 = 1.833333333 + 0.25

Combine like terms: 1.833333333 + 0.25 = 2.083333333
0.25 + -0.1666666667r + r2 = 2.083333333

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 2.083333333

Calculate the square root of the right side: 1.443375673

Break this problem into two subproblems by setting 
(r + 0.5) equal to 1.443375673 and -1.443375673.

Subproblem 1

r + 0.5 = 1.443375673 Simplifying r + 0.5 = 1.443375673 Reorder the terms: 0.5 + r = 1.443375673 Solving 0.5 + r = 1.443375673 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 1.443375673 + -0.5 r = 1.443375673 + -0.5 Combine like terms: 1.443375673 + -0.5 = 0.943375673 r = 0.943375673 Simplifying r = 0.943375673

Subproblem 2

r + 0.5 = -1.443375673 Simplifying r + 0.5 = -1.443375673 Reorder the terms: 0.5 + r = -1.443375673 Solving 0.5 + r = -1.443375673 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -1.443375673 + -0.5 r = -1.443375673 + -0.5 Combine like terms: -1.443375673 + -0.5 = -1.943375673 r = -1.943375673 Simplifying r = -1.943375673

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.943375673, -1.943375673}

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