36=r(18.5+r)

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Solution for 36=r(18.5+r) equation:


Simplifying
36 = r(18.5 + r)
36 = (18.5 * r + r * r)
36 = (18.5r + r2)

Solving
36 = 18.5r + r2

Solving for variable 'r'.

Reorder the terms:
36 + -18.5r + -1r2 = 18.5r + -18.5r + r2 + -1r2

Combine like terms: 18.5r + -18.5r = 0.0
36 + -18.5r + -1r2 = 0.0 + r2 + -1r2
36 + -18.5r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
36 + -18.5r + -1r2 = 0

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

Divide each side by '-1'.
-36 + 18.5r + r2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 18.5r + 36 + r2 = 0 + 36

Reorder the terms:
-36 + 36 + 18.5r + r2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 18.5r + r2 = 0 + 36
18.5r + r2 = 0 + 36

Combine like terms: 0 + 36 = 36
18.5r + r2 = 36

The r term is 18.5r.  Take half its coefficient (9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
18.5r + 85.5625 + r2 = 36 + 85.5625

Reorder the terms:
85.5625 + 18.5r + r2 = 36 + 85.5625

Combine like terms: 36 + 85.5625 = 121.5625
85.5625 + 18.5r + r2 = 121.5625

Factor a perfect square on the left side:
(r + 9.25)(r + 9.25) = 121.5625

Calculate the square root of the right side: 11.025538536

Break this problem into two subproblems by setting 
(r + 9.25) equal to 11.025538536 and -11.025538536.

Subproblem 1

r + 9.25 = 11.025538536 Simplifying r + 9.25 = 11.025538536 Reorder the terms: 9.25 + r = 11.025538536 Solving 9.25 + r = 11.025538536 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + r = 11.025538536 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + r = 11.025538536 + -9.25 r = 11.025538536 + -9.25 Combine like terms: 11.025538536 + -9.25 = 1.775538536 r = 1.775538536 Simplifying r = 1.775538536

Subproblem 2

r + 9.25 = -11.025538536 Simplifying r + 9.25 = -11.025538536 Reorder the terms: 9.25 + r = -11.025538536 Solving 9.25 + r = -11.025538536 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + r = -11.025538536 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + r = -11.025538536 + -9.25 r = -11.025538536 + -9.25 Combine like terms: -11.025538536 + -9.25 = -20.275538536 r = -20.275538536 Simplifying r = -20.275538536

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.775538536, -20.275538536}

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