-3r^2+20r-4=0

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Solution for -3r^2+20r-4=0 equation: 


Simplifying
-3r2 + 20r + -4 = 0

Reorder the terms:
-4 + 20r + -3r2 = 0

Solving
-4 + 20r + -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'.
1.333333333 + -6.666666667r + r2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -6.666666667r + -1.333333333 + r2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -6.666666667r + r2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -6.666666667r + r2 = 0 + -1.333333333
-6.666666667r + r2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-6.666666667r + r2 = -1.333333333

The r term is -6.666666667r.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667r + 11.11111112 + r2 = -1.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667r + r2 = -1.333333333 + 11.11111112

Combine like terms: -1.333333333 + 11.11111112 = 9.777777787
11.11111112 + -6.666666667r + r2 = 9.777777787

Factor a perfect square on the left side:
(r + -3.333333334)(r + -3.333333334) = 9.777777787

Calculate the square root of the right side: 3.126943841

Break this problem into two subproblems by setting 
(r + -3.333333334) equal to 3.126943841 and -3.126943841.


Subproblem 1
r + -3.333333334 = 3.126943841

Simplifying
r + -3.333333334 = 3.126943841

Reorder the terms:
-3.333333334 + r = 3.126943841

Solving
-3.333333334 + r = 3.126943841

Solving for variable 'r'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + r = 3.126943841 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + r = 3.126943841 + 3.333333334
r = 3.126943841 + 3.333333334

Combine like terms: 3.126943841 + 3.333333334 = 6.460277175
r = 6.460277175

Simplifying
r = 6.460277175


Subproblem 2
r + -3.333333334 = -3.126943841

Simplifying
r + -3.333333334 = -3.126943841

Reorder the terms:
-3.333333334 + r = -3.126943841

Solving
-3.333333334 + r = -3.126943841

Solving for variable 'r'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + r = -3.126943841 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + r = -3.126943841 + 3.333333334
r = -3.126943841 + 3.333333334

Combine like terms: -3.126943841 + 3.333333334 = 0.206389493
r = 0.206389493

Simplifying
r = 0.206389493


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.460277175, 0.206389493}

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