576=r^2+256+32r+r^2

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Solution for 576=r^2+256+32r+r^2 equation: 


Simplifying
576 = r2 + 256 + 32r + r2

Reorder the terms:
576 = 256 + 32r + r2 + r2

Combine like terms: r2 + r2 = 2r2
576 = 256 + 32r + 2r2

Solving
576 = 256 + 32r + 2r2

Solving for variable 'r'.

Combine like terms: 576 + -256 = 320
320 + -32r + -2r2 = 256 + 32r + 2r2 + -256 + -32r + -2r2

Reorder the terms:
320 + -32r + -2r2 = 256 + -256 + 32r + -32r + 2r2 + -2r2

Combine like terms: 256 + -256 = 0
320 + -32r + -2r2 = 0 + 32r + -32r + 2r2 + -2r2
320 + -32r + -2r2 = 32r + -32r + 2r2 + -2r2

Combine like terms: 32r + -32r = 0
320 + -32r + -2r2 = 0 + 2r2 + -2r2
320 + -32r + -2r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
320 + -32r + -2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(160 + -16r + -1r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(160 + -16r + -1r2)' equal to zero and attempt to solve:

Simplifying
160 + -16r + -1r2 = 0

Solving
160 + -16r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-160 + 16r + r2 = 0

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 16r + 160 + r2 = 0 + 160

Reorder the terms:
-160 + 160 + 16r + r2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 16r + r2 = 0 + 160
16r + r2 = 0 + 160

Combine like terms: 0 + 160 = 160
16r + r2 = 160

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 = 160 + 64

Reorder the terms:
64 + 16r + r2 = 160 + 64

Combine like terms: 160 + 64 = 224
64 + 16r + r2 = 224

Factor a perfect square on the left side:
(r + 8)(r + 8) = 224

Calculate the square root of the right side: 14.966629547

Break this problem into two subproblems by setting 
(r + 8) equal to 14.966629547 and -14.966629547.


Subproblem 1
r + 8 = 14.966629547

Simplifying
r + 8 = 14.966629547

Reorder the terms:
8 + r = 14.966629547

Solving
8 + r = 14.966629547

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 = 14.966629547 + -8

Combine like terms: 8 + -8 = 0
0 + r = 14.966629547 + -8
r = 14.966629547 + -8

Combine like terms: 14.966629547 + -8 = 6.966629547
r = 6.966629547

Simplifying
r = 6.966629547


Subproblem 2
r + 8 = -14.966629547

Simplifying
r + 8 = -14.966629547

Reorder the terms:
8 + r = -14.966629547

Solving
8 + r = -14.966629547

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 = -14.966629547 + -8

Combine like terms: 8 + -8 = 0
0 + r = -14.966629547 + -8
r = -14.966629547 + -8

Combine like terms: -14.966629547 + -8 = -22.966629547
r = -22.966629547

Simplifying
r = -22.966629547


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.966629547, -22.966629547}
Solution
r = {6.966629547, -22.966629547}

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