1270.444=6.28r^2+137.532r

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Solution for 1270.444=6.28r^2+137.532r equation: 


Simplifying
1270.444 = 6.28r2 + 137.532r

Reorder the terms:
1270.444 = 137.532r + 6.28r2

Solving
1270.444 = 137.532r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
1270.444 + -137.532r + -6.28r2 = 137.532r + -137.532r + 6.28r2 + -6.28r2

Combine like terms: 137.532r + -137.532r = 0.000
1270.444 + -137.532r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
1270.444 + -137.532r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
1270.444 + -137.532r + -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'.
-202.3 + 21.9r + r2 = 0

Move the constant term to the right:

Add '202.3' to each side of the equation.
-202.3 + 21.9r + 202.3 + r2 = 0 + 202.3

Reorder the terms:
-202.3 + 202.3 + 21.9r + r2 = 0 + 202.3

Combine like terms: -202.3 + 202.3 = 0.0
0.0 + 21.9r + r2 = 0 + 202.3
21.9r + r2 = 0 + 202.3

Combine like terms: 0 + 202.3 = 202.3
21.9r + r2 = 202.3

The r term is 21.9r.  Take half its coefficient (10.95).
Square it (119.9025) and add it to both sides.

Add '119.9025' to each side of the equation.
21.9r + 119.9025 + r2 = 202.3 + 119.9025

Reorder the terms:
119.9025 + 21.9r + r2 = 202.3 + 119.9025

Combine like terms: 202.3 + 119.9025 = 322.2025
119.9025 + 21.9r + r2 = 322.2025

Factor a perfect square on the left side:
(r + 10.95)(r + 10.95) = 322.2025

Calculate the square root of the right side: 17.95

Break this problem into two subproblems by setting 
(r + 10.95) equal to 17.95 and -17.95.


Subproblem 1
r + 10.95 = 17.95

Simplifying
r + 10.95 = 17.95

Reorder the terms:
10.95 + r = 17.95

Solving
10.95 + r = 17.95

Solving for variable 'r'.

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

Add '-10.95' to each side of the equation.
10.95 + -10.95 + r = 17.95 + -10.95

Combine like terms: 10.95 + -10.95 = 0.00
0.00 + r = 17.95 + -10.95
r = 17.95 + -10.95

Combine like terms: 17.95 + -10.95 = 7
r = 7

Simplifying
r = 7


Subproblem 2
r + 10.95 = -17.95

Simplifying
r + 10.95 = -17.95

Reorder the terms:
10.95 + r = -17.95

Solving
10.95 + r = -17.95

Solving for variable 'r'.

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

Add '-10.95' to each side of the equation.
10.95 + -10.95 + r = -17.95 + -10.95

Combine like terms: 10.95 + -10.95 = 0.00
0.00 + r = -17.95 + -10.95
r = -17.95 + -10.95

Combine like terms: -17.95 + -10.95 = -28.9
r = -28.9

Simplifying
r = -28.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {7, -28.9}

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