3r^2-35r+79=0

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Solution for 3r^2-35r+79=0 equation: 


Simplifying
3r2 + -35r + 79 = 0

Reorder the terms:
79 + -35r + 3r2 = 0

Solving
79 + -35r + 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'.
26.33333333 + -11.66666667r + r2 = 0

Move the constant term to the right:

Add '-26.33333333' to each side of the equation.
26.33333333 + -11.66666667r + -26.33333333 + r2 = 0 + -26.33333333

Reorder the terms:
26.33333333 + -26.33333333 + -11.66666667r + r2 = 0 + -26.33333333

Combine like terms: 26.33333333 + -26.33333333 = 0.00000000
0.00000000 + -11.66666667r + r2 = 0 + -26.33333333
-11.66666667r + r2 = 0 + -26.33333333

Combine like terms: 0 + -26.33333333 = -26.33333333
-11.66666667r + r2 = -26.33333333

The r term is -11.66666667r.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667r + 34.02777780 + r2 = -26.33333333 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667r + r2 = -26.33333333 + 34.02777780

Combine like terms: -26.33333333 + 34.02777780 = 7.69444447
34.02777780 + -11.66666667r + r2 = 7.69444447

Factor a perfect square on the left side:
(r + -5.833333335)(r + -5.833333335) = 7.69444447

Calculate the square root of the right side: 2.773886167

Break this problem into two subproblems by setting 
(r + -5.833333335) equal to 2.773886167 and -2.773886167.


Subproblem 1
r + -5.833333335 = 2.773886167

Simplifying
r + -5.833333335 = 2.773886167

Reorder the terms:
-5.833333335 + r = 2.773886167

Solving
-5.833333335 + r = 2.773886167

Solving for variable 'r'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + r = 2.773886167 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + r = 2.773886167 + 5.833333335
r = 2.773886167 + 5.833333335

Combine like terms: 2.773886167 + 5.833333335 = 8.607219502
r = 8.607219502

Simplifying
r = 8.607219502


Subproblem 2
r + -5.833333335 = -2.773886167

Simplifying
r + -5.833333335 = -2.773886167

Reorder the terms:
-5.833333335 + r = -2.773886167

Solving
-5.833333335 + r = -2.773886167

Solving for variable 'r'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + r = -2.773886167 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + r = -2.773886167 + 5.833333335
r = -2.773886167 + 5.833333335

Combine like terms: -2.773886167 + 5.833333335 = 3.059447168
r = 3.059447168

Simplifying
r = 3.059447168


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.607219502, 3.059447168}

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