r^2-6r-80=5

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Solution for r^2-6r-80=5 equation: 


Simplifying
r2 + -6r + -80 = 5

Reorder the terms:
-80 + -6r + r2 = 5

Solving
-80 + -6r + r2 = 5

Solving for variable 'r'.

Reorder the terms:
-80 + -5 + -6r + r2 = 5 + -5

Combine like terms: -80 + -5 = -85
-85 + -6r + r2 = 5 + -5

Combine like terms: 5 + -5 = 0
-85 + -6r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + -6r + 85 + r2 = 0 + 85

Reorder the terms:
-85 + 85 + -6r + r2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -6r + r2 = 0 + 85
-6r + r2 = 0 + 85

Combine like terms: 0 + 85 = 85
-6r + r2 = 85

The r term is -6r.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6r + 9 + r2 = 85 + 9

Reorder the terms:
9 + -6r + r2 = 85 + 9

Combine like terms: 85 + 9 = 94
9 + -6r + r2 = 94

Factor a perfect square on the left side:
(r + -3)(r + -3) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(r + -3) equal to 9.695359715 and -9.695359715.


Subproblem 1
r + -3 = 9.695359715

Simplifying
r + -3 = 9.695359715

Reorder the terms:
-3 + r = 9.695359715

Solving
-3 + r = 9.695359715

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = 9.695359715 + 3

Combine like terms: -3 + 3 = 0
0 + r = 9.695359715 + 3
r = 9.695359715 + 3

Combine like terms: 9.695359715 + 3 = 12.695359715
r = 12.695359715

Simplifying
r = 12.695359715


Subproblem 2
r + -3 = -9.695359715

Simplifying
r + -3 = -9.695359715

Reorder the terms:
-3 + r = -9.695359715

Solving
-3 + r = -9.695359715

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = -9.695359715 + 3

Combine like terms: -3 + 3 = 0
0 + r = -9.695359715 + 3
r = -9.695359715 + 3

Combine like terms: -9.695359715 + 3 = -6.695359715
r = -6.695359715

Simplifying
r = -6.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {12.695359715, -6.695359715}

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