3r^2-17r-10=

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Solution for 3r^2-17r-10= equation: 


Simplifying
3r2 + -17r + -10 = 0

Reorder the terms:
-10 + -17r + 3r2 = 0

Solving
-10 + -17r + 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'.
-3.333333333 + -5.666666667r + r2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -5.666666667r + 3.333333333 + r2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -5.666666667r + r2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -5.666666667r + r2 = 0 + 3.333333333
-5.666666667r + r2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-5.666666667r + r2 = 3.333333333

The r term is -5.666666667r.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667r + 8.027777782 + r2 = 3.333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667r + r2 = 3.333333333 + 8.027777782

Combine like terms: 3.333333333 + 8.027777782 = 11.361111115
8.027777782 + -5.666666667r + r2 = 11.361111115

Factor a perfect square on the left side:
(r + -2.833333334)(r + -2.833333334) = 11.361111115

Calculate the square root of the right side: 3.370624737

Break this problem into two subproblems by setting 
(r + -2.833333334) equal to 3.370624737 and -3.370624737.


Subproblem 1
r + -2.833333334 = 3.370624737

Simplifying
r + -2.833333334 = 3.370624737

Reorder the terms:
-2.833333334 + r = 3.370624737

Solving
-2.833333334 + r = 3.370624737

Solving for variable 'r'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + r = 3.370624737 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + r = 3.370624737 + 2.833333334
r = 3.370624737 + 2.833333334

Combine like terms: 3.370624737 + 2.833333334 = 6.203958071
r = 6.203958071

Simplifying
r = 6.203958071


Subproblem 2
r + -2.833333334 = -3.370624737

Simplifying
r + -2.833333334 = -3.370624737

Reorder the terms:
-2.833333334 + r = -3.370624737

Solving
-2.833333334 + r = -3.370624737

Solving for variable 'r'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + r = -3.370624737 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + r = -3.370624737 + 2.833333334
r = -3.370624737 + 2.833333334

Combine like terms: -3.370624737 + 2.833333334 = -0.537291403
r = -0.537291403

Simplifying
r = -0.537291403


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.203958071, -0.537291403}

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