36r-360-24r+240=r^2+100

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Solution for 36r-360-24r+240=r^2+100 equation: 


Simplifying
36r + -360 + -24r + 240 = r2 + 100

Reorder the terms:
-360 + 240 + 36r + -24r = r2 + 100

Combine like terms: -360 + 240 = -120
-120 + 36r + -24r = r2 + 100

Combine like terms: 36r + -24r = 12r
-120 + 12r = r2 + 100

Reorder the terms:
-120 + 12r = 100 + r2

Solving
-120 + 12r = 100 + r2

Solving for variable 'r'.

Reorder the terms:
-120 + -100 + 12r + -1r2 = 100 + r2 + -100 + -1r2

Combine like terms: -120 + -100 = -220
-220 + 12r + -1r2 = 100 + r2 + -100 + -1r2

Reorder the terms:
-220 + 12r + -1r2 = 100 + -100 + r2 + -1r2

Combine like terms: 100 + -100 = 0
-220 + 12r + -1r2 = 0 + r2 + -1r2
-220 + 12r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-220 + 12r + -1r2 = 0

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

Divide each side by '-1'.
220 + -12r + r2 = 0

Move the constant term to the right:

Add '-220' to each side of the equation.
220 + -12r + -220 + r2 = 0 + -220

Reorder the terms:
220 + -220 + -12r + r2 = 0 + -220

Combine like terms: 220 + -220 = 0
0 + -12r + r2 = 0 + -220
-12r + r2 = 0 + -220

Combine like terms: 0 + -220 = -220
-12r + r2 = -220

The r term is -12r.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12r + 36 + r2 = -220 + 36

Reorder the terms:
36 + -12r + r2 = -220 + 36

Combine like terms: -220 + 36 = -184
36 + -12r + r2 = -184

Factor a perfect square on the left side:
(r + -6)(r + -6) = -184

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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