11124.392=6.28r^2+547.616r

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Solution for 11124.392=6.28r^2+547.616r equation:


Simplifying
11124.392 = 6.28r2 + 547.616r

Reorder the terms:
11124.392 = 547.616r + 6.28r2

Solving
11124.392 = 547.616r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
11124.392 + -547.616r + -6.28r2 = 547.616r + -547.616r + 6.28r2 + -6.28r2

Combine like terms: 547.616r + -547.616r = 0.000
11124.392 + -547.616r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
11124.392 + -547.616r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
11124.392 + -547.616r + -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'.
-1771.4 + 87.2r + r2 = 0

Move the constant term to the right:

Add '1771.4' to each side of the equation.
-1771.4 + 87.2r + 1771.4 + r2 = 0 + 1771.4

Reorder the terms:
-1771.4 + 1771.4 + 87.2r + r2 = 0 + 1771.4

Combine like terms: -1771.4 + 1771.4 = 0.0
0.0 + 87.2r + r2 = 0 + 1771.4
87.2r + r2 = 0 + 1771.4

Combine like terms: 0 + 1771.4 = 1771.4
87.2r + r2 = 1771.4

The r term is 87.2r.  Take half its coefficient (43.6).
Square it (1900.96) and add it to both sides.

Add '1900.96' to each side of the equation.
87.2r + 1900.96 + r2 = 1771.4 + 1900.96

Reorder the terms:
1900.96 + 87.2r + r2 = 1771.4 + 1900.96

Combine like terms: 1771.4 + 1900.96 = 3672.36
1900.96 + 87.2r + r2 = 3672.36

Factor a perfect square on the left side:
(r + 43.6)(r + 43.6) = 3672.36

Calculate the square root of the right side: 60.6

Break this problem into two subproblems by setting 
(r + 43.6) equal to 60.6 and -60.6.

Subproblem 1

r + 43.6 = 60.6 Simplifying r + 43.6 = 60.6 Reorder the terms: 43.6 + r = 60.6 Solving 43.6 + r = 60.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-43.6' to each side of the equation. 43.6 + -43.6 + r = 60.6 + -43.6 Combine like terms: 43.6 + -43.6 = 0.0 0.0 + r = 60.6 + -43.6 r = 60.6 + -43.6 Combine like terms: 60.6 + -43.6 = 17 r = 17 Simplifying r = 17

Subproblem 2

r + 43.6 = -60.6 Simplifying r + 43.6 = -60.6 Reorder the terms: 43.6 + r = -60.6 Solving 43.6 + r = -60.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-43.6' to each side of the equation. 43.6 + -43.6 + r = -60.6 + -43.6 Combine like terms: 43.6 + -43.6 = 0.0 0.0 + r = -60.6 + -43.6 r = -60.6 + -43.6 Combine like terms: -60.6 + -43.6 = -104.2 r = -104.2 Simplifying r = -104.2

Solution

The solution to the problem is based on the solutions from the subproblems. r = {17, -104.2}

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