3r^2+11r-8=

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Solution for 3r^2+11r-8= equation: 


Simplifying
3r2 + 11r + -8 = 0

Reorder the terms:
-8 + 11r + 3r2 = 0

Solving
-8 + 11r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
-2.666666667 + 3.666666667r + r2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 3.666666667r + 2.666666667 + r2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 3.666666667r + r2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 3.666666667r + r2 = 0 + 2.666666667
3.666666667r + r2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
3.666666667r + r2 = 2.666666667

The r term is 3.666666667r.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667r + 3.361111114 + r2 = 2.666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667r + r2 = 2.666666667 + 3.361111114

Combine like terms: 2.666666667 + 3.361111114 = 6.027777781
3.361111114 + 3.666666667r + r2 = 6.027777781

Factor a perfect square on the left side:
(r + 1.833333334)(r + 1.833333334) = 6.027777781

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(r + 1.833333334) equal to 2.455153311 and -2.455153311.


Subproblem 1
r + 1.833333334 = 2.455153311

Simplifying
r + 1.833333334 = 2.455153311

Reorder the terms:
1.833333334 + r = 2.455153311

Solving
1.833333334 + r = 2.455153311

Solving for variable 'r'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + r = 2.455153311 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + r = 2.455153311 + -1.833333334
r = 2.455153311 + -1.833333334

Combine like terms: 2.455153311 + -1.833333334 = 0.621819977
r = 0.621819977

Simplifying
r = 0.621819977


Subproblem 2
r + 1.833333334 = -2.455153311

Simplifying
r + 1.833333334 = -2.455153311

Reorder the terms:
1.833333334 + r = -2.455153311

Solving
1.833333334 + r = -2.455153311

Solving for variable 'r'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + r = -2.455153311 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + r = -2.455153311 + -1.833333334
r = -2.455153311 + -1.833333334

Combine like terms: -2.455153311 + -1.833333334 = -4.288486645
r = -4.288486645

Simplifying
r = -4.288486645


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.621819977, -4.288486645}

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