2r^2-32r+64=

Solution for 2r^2-32r+64= equation:

Simplifying
2r2 + -32r + 64 = 0

Reorder the terms:
64 + -32r + 2r2 = 0

Solving
64 + -32r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + -16r + r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(32 + -16r + r2)' equal to zero and attempt to solve:

Simplifying
32 + -16r + r2 = 0

Solving
32 + -16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -16r + -32 + r2 = 0 + -32

Reorder the terms:
32 + -32 + -16r + r2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -16r + r2 = 0 + -32
-16r + r2 = 0 + -32

Combine like terms: 0 + -32 = -32
-16r + r2 = -32

The r term is -16r.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16r + 64 + r2 = -32 + 64

Reorder the terms:
64 + -16r + r2 = -32 + 64

Combine like terms: -32 + 64 = 32
64 + -16r + r2 = 32

Factor a perfect square on the left side:
(r + -8)(r + -8) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(r + -8) equal to 5.656854249 and -5.656854249.

Subproblem 1
r + -8 = 5.656854249

Simplifying
r + -8 = 5.656854249

Reorder the terms:
-8 + r = 5.656854249

Solving
-8 + r = 5.656854249

Solving for variable 'r'.

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

Add '8' to each side of the equation.
-8 + 8 + r = 5.656854249 + 8

Combine like terms: -8 + 8 = 0
0 + r = 5.656854249 + 8
r = 5.656854249 + 8

Combine like terms: 5.656854249 + 8 = 13.656854249
r = 13.656854249

Simplifying
r = 13.656854249

Subproblem 2
r + -8 = -5.656854249

Simplifying
r + -8 = -5.656854249

Reorder the terms:
-8 + r = -5.656854249

Solving
-8 + r = -5.656854249

Solving for variable 'r'.

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

Add '8' to each side of the equation.
-8 + 8 + r = -5.656854249 + 8

Combine like terms: -8 + 8 = 0
0 + r = -5.656854249 + 8
r = -5.656854249 + 8

Combine like terms: -5.656854249 + 8 = 2.343145751
r = 2.343145751

Simplifying
r = 2.343145751

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {13.656854249, 2.343145751}
Solution
r = {13.656854249, 2.343145751}