-8r^2+10r+9=0

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Solution for -8r^2+10r+9=0 equation: 


Simplifying
-8r2 + 10r + 9 = 0

Reorder the terms:
9 + 10r + -8r2 = 0

Solving
9 + 10r + -8r2 = 0

Solving for variable 'r'.

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

Divide each side by '-8'.
-1.125 + -1.25r + r2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -1.25r + 1.125 + r2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -1.25r + r2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -1.25r + r2 = 0 + 1.125
-1.25r + r2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-1.25r + r2 = 1.125

The r term is -1.25r.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25r + 0.390625 + r2 = 1.125 + 0.390625

Reorder the terms:
0.390625 + -1.25r + r2 = 1.125 + 0.390625

Combine like terms: 1.125 + 0.390625 = 1.515625
0.390625 + -1.25r + r2 = 1.515625

Factor a perfect square on the left side:
(r + -0.625)(r + -0.625) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(r + -0.625) equal to 1.231107225 and -1.231107225.


Subproblem 1
r + -0.625 = 1.231107225

Simplifying
r + -0.625 = 1.231107225

Reorder the terms:
-0.625 + r = 1.231107225

Solving
-0.625 + r = 1.231107225

Solving for variable 'r'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + r = 1.231107225 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + r = 1.231107225 + 0.625
r = 1.231107225 + 0.625

Combine like terms: 1.231107225 + 0.625 = 1.856107225
r = 1.856107225

Simplifying
r = 1.856107225


Subproblem 2
r + -0.625 = -1.231107225

Simplifying
r + -0.625 = -1.231107225

Reorder the terms:
-0.625 + r = -1.231107225

Solving
-0.625 + r = -1.231107225

Solving for variable 'r'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + r = -1.231107225 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + r = -1.231107225 + 0.625
r = -1.231107225 + 0.625

Combine like terms: -1.231107225 + 0.625 = -0.606107225
r = -0.606107225

Simplifying
r = -0.606107225


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.856107225, -0.606107225}

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