0.09r^2+2.44r=9.03

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Solution for 0.09r^2+2.44r=9.03 equation:


Simplifying
0.09r2 + 2.44r = 9.03

Reorder the terms:
2.44r + 0.09r2 = 9.03

Solving
2.44r + 0.09r2 = 9.03

Solving for variable 'r'.

Reorder the terms:
-9.03 + 2.44r + 0.09r2 = 9.03 + -9.03

Combine like terms: 9.03 + -9.03 = 0.00
-9.03 + 2.44r + 0.09r2 = 0.00

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

Divide each side by '0.09'.
-100.3333333 + 27.11111111r + r2 = 0

Move the constant term to the right:

Add '100.3333333' to each side of the equation.
-100.3333333 + 27.11111111r + 100.3333333 + r2 = 0 + 100.3333333

Reorder the terms:
-100.3333333 + 100.3333333 + 27.11111111r + r2 = 0 + 100.3333333

Combine like terms: -100.3333333 + 100.3333333 = 0.0000000
0.0000000 + 27.11111111r + r2 = 0 + 100.3333333
27.11111111r + r2 = 0 + 100.3333333

Combine like terms: 0 + 100.3333333 = 100.3333333
27.11111111r + r2 = 100.3333333

The r term is 27.11111111r.  Take half its coefficient (13.55555556).
Square it (183.7530865) and add it to both sides.

Add '183.7530865' to each side of the equation.
27.11111111r + 183.7530865 + r2 = 100.3333333 + 183.7530865

Reorder the terms:
183.7530865 + 27.11111111r + r2 = 100.3333333 + 183.7530865

Combine like terms: 100.3333333 + 183.7530865 = 284.0864198
183.7530865 + 27.11111111r + r2 = 284.0864198

Factor a perfect square on the left side:
(r + 13.55555556)(r + 13.55555556) = 284.0864198

Calculate the square root of the right side: 16.854863387

Break this problem into two subproblems by setting 
(r + 13.55555556) equal to 16.854863387 and -16.854863387.

Subproblem 1

r + 13.55555556 = 16.854863387 Simplifying r + 13.55555556 = 16.854863387 Reorder the terms: 13.55555556 + r = 16.854863387 Solving 13.55555556 + r = 16.854863387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13.55555556' to each side of the equation. 13.55555556 + -13.55555556 + r = 16.854863387 + -13.55555556 Combine like terms: 13.55555556 + -13.55555556 = 0.00000000 0.00000000 + r = 16.854863387 + -13.55555556 r = 16.854863387 + -13.55555556 Combine like terms: 16.854863387 + -13.55555556 = 3.299307827 r = 3.299307827 Simplifying r = 3.299307827

Subproblem 2

r + 13.55555556 = -16.854863387 Simplifying r + 13.55555556 = -16.854863387 Reorder the terms: 13.55555556 + r = -16.854863387 Solving 13.55555556 + r = -16.854863387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13.55555556' to each side of the equation. 13.55555556 + -13.55555556 + r = -16.854863387 + -13.55555556 Combine like terms: 13.55555556 + -13.55555556 = 0.00000000 0.00000000 + r = -16.854863387 + -13.55555556 r = -16.854863387 + -13.55555556 Combine like terms: -16.854863387 + -13.55555556 = -30.410418947 r = -30.410418947 Simplifying r = -30.410418947

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.299307827, -30.410418947}

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