4r^2-12r-64=

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Solution for 4r^2-12r-64= equation: 


Simplifying
4r2 + -12r + -64 = 0

Reorder the terms:
-64 + -12r + 4r2 = 0

Solving
-64 + -12r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -3r + r2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -3r + r2)' equal to zero and attempt to solve:

Simplifying
-16 + -3r + r2 = 0

Solving
-16 + -3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -3r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + -3r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3r + r2 = 0 + 16
-3r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
-3r + r2 = 16

The r term is -3r.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3r + 2.25 + r2 = 16 + 2.25

Reorder the terms:
2.25 + -3r + r2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + -3r + r2 = 18.25

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(r + -1.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
r + -1.5 = 4.272001873

Simplifying
r + -1.5 = 4.272001873

Reorder the terms:
-1.5 + r = 4.272001873

Solving
-1.5 + r = 4.272001873

Solving for variable 'r'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + r = 4.272001873 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 4.272001873 + 1.5
r = 4.272001873 + 1.5

Combine like terms: 4.272001873 + 1.5 = 5.772001873
r = 5.772001873

Simplifying
r = 5.772001873


Subproblem 2
r + -1.5 = -4.272001873

Simplifying
r + -1.5 = -4.272001873

Reorder the terms:
-1.5 + r = -4.272001873

Solving
-1.5 + r = -4.272001873

Solving for variable 'r'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + r = -4.272001873 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -4.272001873 + 1.5
r = -4.272001873 + 1.5

Combine like terms: -4.272001873 + 1.5 = -2.772001873
r = -2.772001873

Simplifying
r = -2.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.772001873, -2.772001873}
Solution
r = {5.772001873, -2.772001873}

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