8r^2-16r-128=0

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Solution for 8r^2-16r-128=0 equation: 


Simplifying
8r2 + -16r + -128 = 0

Reorder the terms:
-128 + -16r + 8r2 = 0

Solving
-128 + -16r + 8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-16 + -2r + r2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-16 + -2r + r2)' equal to zero and attempt to solve:

Simplifying
-16 + -2r + r2 = 0

Solving
-16 + -2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -2r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + -2r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -2r + r2 = 0 + 16
-2r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
-2r + r2 = 16

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 16 + 1

Reorder the terms:
1 + -2r + r2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + -2r + r2 = 17

Factor a perfect square on the left side:
(r + -1)(r + -1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(r + -1) equal to 4.123105626 and -4.123105626.


Subproblem 1
r + -1 = 4.123105626

Simplifying
r + -1 = 4.123105626

Reorder the terms:
-1 + r = 4.123105626

Solving
-1 + r = 4.123105626

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = 4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + r = 4.123105626 + 1
r = 4.123105626 + 1

Combine like terms: 4.123105626 + 1 = 5.123105626
r = 5.123105626

Simplifying
r = 5.123105626


Subproblem 2
r + -1 = -4.123105626

Simplifying
r + -1 = -4.123105626

Reorder the terms:
-1 + r = -4.123105626

Solving
-1 + r = -4.123105626

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = -4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + r = -4.123105626 + 1
r = -4.123105626 + 1

Combine like terms: -4.123105626 + 1 = -3.123105626
r = -3.123105626

Simplifying
r = -3.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.123105626, -3.123105626}
Solution
r = {5.123105626, -3.123105626}

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