12r^2-17r-2=0

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Solution for 12r^2-17r-2=0 equation: 


Simplifying
12r2 + -17r + -2 = 0

Reorder the terms:
-2 + -17r + 12r2 = 0

Solving
-2 + -17r + 12r2 = 0

Solving for variable 'r'.

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

Divide each side by '12'.
-0.1666666667 + -1.416666667r + r2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -1.416666667r + 0.1666666667 + r2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -1.416666667r + r2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -1.416666667r + r2 = 0 + 0.1666666667
-1.416666667r + r2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-1.416666667r + r2 = 0.1666666667

The r term is -1.416666667r.  Take half its coefficient (-0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
-1.416666667r + 0.5017361113 + r2 = 0.1666666667 + 0.5017361113

Reorder the terms:
0.5017361113 + -1.416666667r + r2 = 0.1666666667 + 0.5017361113

Combine like terms: 0.1666666667 + 0.5017361113 = 0.668402778
0.5017361113 + -1.416666667r + r2 = 0.668402778

Factor a perfect square on the left side:
(r + -0.7083333335)(r + -0.7083333335) = 0.668402778

Calculate the square root of the right side: 0.817559036

Break this problem into two subproblems by setting 
(r + -0.7083333335) equal to 0.817559036 and -0.817559036.


Subproblem 1
r + -0.7083333335 = 0.817559036

Simplifying
r + -0.7083333335 = 0.817559036

Reorder the terms:
-0.7083333335 + r = 0.817559036

Solving
-0.7083333335 + r = 0.817559036

Solving for variable 'r'.

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

Add '0.7083333335' to each side of the equation.
-0.7083333335 + 0.7083333335 + r = 0.817559036 + 0.7083333335

Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000
0.0000000000 + r = 0.817559036 + 0.7083333335
r = 0.817559036 + 0.7083333335

Combine like terms: 0.817559036 + 0.7083333335 = 1.5258923695
r = 1.5258923695

Simplifying
r = 1.5258923695


Subproblem 2
r + -0.7083333335 = -0.817559036

Simplifying
r + -0.7083333335 = -0.817559036

Reorder the terms:
-0.7083333335 + r = -0.817559036

Solving
-0.7083333335 + r = -0.817559036

Solving for variable 'r'.

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

Add '0.7083333335' to each side of the equation.
-0.7083333335 + 0.7083333335 + r = -0.817559036 + 0.7083333335

Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000
0.0000000000 + r = -0.817559036 + 0.7083333335
r = -0.817559036 + 0.7083333335

Combine like terms: -0.817559036 + 0.7083333335 = -0.1092257025
r = -0.1092257025

Simplifying
r = -0.1092257025


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.5258923695, -0.1092257025}

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