4r^2-220r+1160=0

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Solution for 4r^2-220r+1160=0 equation: 


Simplifying
4r2 + -220r + 1160 = 0

Reorder the terms:
1160 + -220r + 4r2 = 0

Solving
1160 + -220r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(290 + -55r + r2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(290 + -55r + r2)' equal to zero and attempt to solve:

Simplifying
290 + -55r + r2 = 0

Solving
290 + -55r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-290' to each side of the equation.
290 + -55r + -290 + r2 = 0 + -290

Reorder the terms:
290 + -290 + -55r + r2 = 0 + -290

Combine like terms: 290 + -290 = 0
0 + -55r + r2 = 0 + -290
-55r + r2 = 0 + -290

Combine like terms: 0 + -290 = -290
-55r + r2 = -290

The r term is -55r.  Take half its coefficient (-27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
-55r + 756.25 + r2 = -290 + 756.25

Reorder the terms:
756.25 + -55r + r2 = -290 + 756.25

Combine like terms: -290 + 756.25 = 466.25
756.25 + -55r + r2 = 466.25

Factor a perfect square on the left side:
(r + -27.5)(r + -27.5) = 466.25

Calculate the square root of the right side: 21.592822882

Break this problem into two subproblems by setting 
(r + -27.5) equal to 21.592822882 and -21.592822882.


Subproblem 1
r + -27.5 = 21.592822882

Simplifying
r + -27.5 = 21.592822882

Reorder the terms:
-27.5 + r = 21.592822882

Solving
-27.5 + r = 21.592822882

Solving for variable 'r'.

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

Add '27.5' to each side of the equation.
-27.5 + 27.5 + r = 21.592822882 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + r = 21.592822882 + 27.5
r = 21.592822882 + 27.5

Combine like terms: 21.592822882 + 27.5 = 49.092822882
r = 49.092822882

Simplifying
r = 49.092822882


Subproblem 2
r + -27.5 = -21.592822882

Simplifying
r + -27.5 = -21.592822882

Reorder the terms:
-27.5 + r = -21.592822882

Solving
-27.5 + r = -21.592822882

Solving for variable 'r'.

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

Add '27.5' to each side of the equation.
-27.5 + 27.5 + r = -21.592822882 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + r = -21.592822882 + 27.5
r = -21.592822882 + 27.5

Combine like terms: -21.592822882 + 27.5 = 5.907177118
r = 5.907177118

Simplifying
r = 5.907177118


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {49.092822882, 5.907177118}
Solution
r = {49.092822882, 5.907177118}

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