3=10r^2+110r

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Solution for 3=10r^2+110r equation:


Simplifying
3 = 10r2 + 110r

Reorder the terms:
3 = 110r + 10r2

Solving
3 = 110r + 10r2

Solving for variable 'r'.

Reorder the terms:
3 + -110r + -10r2 = 110r + -110r + 10r2 + -10r2

Combine like terms: 110r + -110r = 0
3 + -110r + -10r2 = 0 + 10r2 + -10r2
3 + -110r + -10r2 = 10r2 + -10r2

Combine like terms: 10r2 + -10r2 = 0
3 + -110r + -10r2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.3 + 11r + r2 = 0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 11r + 0.3 + r2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 11r + r2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 11r + r2 = 0 + 0.3
11r + r2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
11r + r2 = 0.3

The r term is 11r.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11r + 30.25 + r2 = 0.3 + 30.25

Reorder the terms:
30.25 + 11r + r2 = 0.3 + 30.25

Combine like terms: 0.3 + 30.25 = 30.55
30.25 + 11r + r2 = 30.55

Factor a perfect square on the left side:
(r + 5.5)(r + 5.5) = 30.55

Calculate the square root of the right side: 5.527205442

Break this problem into two subproblems by setting 
(r + 5.5) equal to 5.527205442 and -5.527205442.

Subproblem 1

r + 5.5 = 5.527205442 Simplifying r + 5.5 = 5.527205442 Reorder the terms: 5.5 + r = 5.527205442 Solving 5.5 + r = 5.527205442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + r = 5.527205442 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + r = 5.527205442 + -5.5 r = 5.527205442 + -5.5 Combine like terms: 5.527205442 + -5.5 = 0.027205442 r = 0.027205442 Simplifying r = 0.027205442

Subproblem 2

r + 5.5 = -5.527205442 Simplifying r + 5.5 = -5.527205442 Reorder the terms: 5.5 + r = -5.527205442 Solving 5.5 + r = -5.527205442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + r = -5.527205442 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + r = -5.527205442 + -5.5 r = -5.527205442 + -5.5 Combine like terms: -5.527205442 + -5.5 = -11.027205442 r = -11.027205442 Simplifying r = -11.027205442

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.027205442, -11.027205442}

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