3150.048=6.28r^2+626.116r

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Solution for 3150.048=6.28r^2+626.116r equation: 


Simplifying
3150.048 = 6.28r2 + 626.116r

Reorder the terms:
3150.048 = 626.116r + 6.28r2

Solving
3150.048 = 626.116r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3150.048 + -626.116r + -6.28r2 = 626.116r + -626.116r + 6.28r2 + -6.28r2

Combine like terms: 626.116r + -626.116r = 0.000
3150.048 + -626.116r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
3150.048 + -626.116r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3150.048 + -626.116r + -6.28r2 = 0.00

Begin completing the square.  Divide all terms by
-6.28 the coefficient of the squared term: 

Divide each side by '-6.28'.
-501.6 + 99.7r + r2 = 0

Move the constant term to the right:

Add '501.6' to each side of the equation.
-501.6 + 99.7r + 501.6 + r2 = 0 + 501.6

Reorder the terms:
-501.6 + 501.6 + 99.7r + r2 = 0 + 501.6

Combine like terms: -501.6 + 501.6 = 0.0
0.0 + 99.7r + r2 = 0 + 501.6
99.7r + r2 = 0 + 501.6

Combine like terms: 0 + 501.6 = 501.6
99.7r + r2 = 501.6

The r term is 99.7r.  Take half its coefficient (49.85).
Square it (2485.0225) and add it to both sides.

Add '2485.0225' to each side of the equation.
99.7r + 2485.0225 + r2 = 501.6 + 2485.0225

Reorder the terms:
2485.0225 + 99.7r + r2 = 501.6 + 2485.0225

Combine like terms: 501.6 + 2485.0225 = 2986.6225
2485.0225 + 99.7r + r2 = 2986.6225

Factor a perfect square on the left side:
(r + 49.85)(r + 49.85) = 2986.6225

Calculate the square root of the right side: 54.65

Break this problem into two subproblems by setting 
(r + 49.85) equal to 54.65 and -54.65.


Subproblem 1
r + 49.85 = 54.65

Simplifying
r + 49.85 = 54.65

Reorder the terms:
49.85 + r = 54.65

Solving
49.85 + r = 54.65

Solving for variable 'r'.

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

Add '-49.85' to each side of the equation.
49.85 + -49.85 + r = 54.65 + -49.85

Combine like terms: 49.85 + -49.85 = 0.00
0.00 + r = 54.65 + -49.85
r = 54.65 + -49.85

Combine like terms: 54.65 + -49.85 = 4.8
r = 4.8

Simplifying
r = 4.8


Subproblem 2
r + 49.85 = -54.65

Simplifying
r + 49.85 = -54.65

Reorder the terms:
49.85 + r = -54.65

Solving
49.85 + r = -54.65

Solving for variable 'r'.

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

Add '-49.85' to each side of the equation.
49.85 + -49.85 + r = -54.65 + -49.85

Combine like terms: 49.85 + -49.85 = 0.00
0.00 + r = -54.65 + -49.85
r = -54.65 + -49.85

Combine like terms: -54.65 + -49.85 = -104.5
r = -104.5

Simplifying
r = -104.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.8, -104.5}

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