80r^2-70r+10=0

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Solution for 80r^2-70r+10=0 equation: 


Simplifying
80r2 + -70r + 10 = 0

Reorder the terms:
10 + -70r + 80r2 = 0

Solving
10 + -70r + 80r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -7r + 8r2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(1 + -7r + 8r2)' equal to zero and attempt to solve:

Simplifying
1 + -7r + 8r2 = 0

Solving
1 + -7r + 8r2 = 0

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

Divide each side by '8'.
0.125 + -0.875r + r2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -0.875r + -0.125 + r2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -0.875r + r2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -0.875r + r2 = 0 + -0.125
-0.875r + r2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-0.875r + r2 = -0.125

The r term is -0.875r.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875r + 0.19140625 + r2 = -0.125 + 0.19140625

Reorder the terms:
0.19140625 + -0.875r + r2 = -0.125 + 0.19140625

Combine like terms: -0.125 + 0.19140625 = 0.06640625
0.19140625 + -0.875r + r2 = 0.06640625

Factor a perfect square on the left side:
(r + -0.4375)(r + -0.4375) = 0.06640625

Calculate the square root of the right side: 0.257694102

Break this problem into two subproblems by setting 
(r + -0.4375) equal to 0.257694102 and -0.257694102.


Subproblem 1
r + -0.4375 = 0.257694102

Simplifying
r + -0.4375 = 0.257694102

Reorder the terms:
-0.4375 + r = 0.257694102

Solving
-0.4375 + r = 0.257694102

Solving for variable 'r'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + r = 0.257694102 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + r = 0.257694102 + 0.4375
r = 0.257694102 + 0.4375

Combine like terms: 0.257694102 + 0.4375 = 0.695194102
r = 0.695194102

Simplifying
r = 0.695194102


Subproblem 2
r + -0.4375 = -0.257694102

Simplifying
r + -0.4375 = -0.257694102

Reorder the terms:
-0.4375 + r = -0.257694102

Solving
-0.4375 + r = -0.257694102

Solving for variable 'r'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + r = -0.257694102 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + r = -0.257694102 + 0.4375
r = -0.257694102 + 0.4375

Combine like terms: -0.257694102 + 0.4375 = 0.179805898
r = 0.179805898

Simplifying
r = 0.179805898


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.695194102, 0.179805898}
Solution
r = {0.695194102, 0.179805898}

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