0.9r^2-4.8r+6.4=0

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Solution for 0.9r^2-4.8r+6.4=0 equation: 


Simplifying
0.9r2 + -4.8r + 6.4 = 0

Reorder the terms:
6.4 + -4.8r + 0.9r2 = 0

Solving
6.4 + -4.8r + 0.9r2 = 0

Solving for variable 'r'.

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

Divide each side by '0.9'.
7.111111111 + -5.333333333r + r2 = 0

Move the constant term to the right:

Add '-7.111111111' to each side of the equation.
7.111111111 + -5.333333333r + -7.111111111 + r2 = 0 + -7.111111111

Reorder the terms:
7.111111111 + -7.111111111 + -5.333333333r + r2 = 0 + -7.111111111

Combine like terms: 7.111111111 + -7.111111111 = 0.000000000
0.000000000 + -5.333333333r + r2 = 0 + -7.111111111
-5.333333333r + r2 = 0 + -7.111111111

Combine like terms: 0 + -7.111111111 = -7.111111111
-5.333333333r + r2 = -7.111111111

The r term is -5.333333333r.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333r + 7.111111113 + r2 = -7.111111111 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333r + r2 = -7.111111111 + 7.111111113

Combine like terms: -7.111111111 + 7.111111113 = 0.000000002
7.111111113 + -5.333333333r + r2 = 0.000000002

Factor a perfect square on the left side:
(r + -2.666666667)(r + -2.666666667) = 0.000000002

Calculate the square root of the right side: 0.000044721

Break this problem into two subproblems by setting 
(r + -2.666666667) equal to 0.000044721 and -0.000044721.


Subproblem 1
r + -2.666666667 = 0.000044721

Simplifying
r + -2.666666667 = 0.000044721

Reorder the terms:
-2.666666667 + r = 0.000044721

Solving
-2.666666667 + r = 0.000044721

Solving for variable 'r'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + r = 0.000044721 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + r = 0.000044721 + 2.666666667
r = 0.000044721 + 2.666666667

Combine like terms: 0.000044721 + 2.666666667 = 2.666711388
r = 2.666711388

Simplifying
r = 2.666711388


Subproblem 2
r + -2.666666667 = -0.000044721

Simplifying
r + -2.666666667 = -0.000044721

Reorder the terms:
-2.666666667 + r = -0.000044721

Solving
-2.666666667 + r = -0.000044721

Solving for variable 'r'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + r = -0.000044721 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + r = -0.000044721 + 2.666666667
r = -0.000044721 + 2.666666667

Combine like terms: -0.000044721 + 2.666666667 = 2.666621946
r = 2.666621946

Simplifying
r = 2.666621946


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.666711388, 2.666621946}

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