0=11r^2-48r-120

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Solution for 0=11r^2-48r-120 equation:


Simplifying
0 = 11r2 + -48r + -120

Reorder the terms:
0 = -120 + -48r + 11r2

Solving
0 = -120 + -48r + 11r2

Solving for variable 'r'.

Combine like terms: 0 + 120 = 120
120 + 48r + -11r2 = -120 + -48r + 11r2 + 120 + 48r + -11r2

Reorder the terms:
120 + 48r + -11r2 = -120 + 120 + -48r + 48r + 11r2 + -11r2

Combine like terms: -120 + 120 = 0
120 + 48r + -11r2 = 0 + -48r + 48r + 11r2 + -11r2
120 + 48r + -11r2 = -48r + 48r + 11r2 + -11r2

Combine like terms: -48r + 48r = 0
120 + 48r + -11r2 = 0 + 11r2 + -11r2
120 + 48r + -11r2 = 11r2 + -11r2

Combine like terms: 11r2 + -11r2 = 0
120 + 48r + -11r2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
-10.90909091 + -4.363636364r + r2 = 0

Move the constant term to the right:

Add '10.90909091' to each side of the equation.
-10.90909091 + -4.363636364r + 10.90909091 + r2 = 0 + 10.90909091

Reorder the terms:
-10.90909091 + 10.90909091 + -4.363636364r + r2 = 0 + 10.90909091

Combine like terms: -10.90909091 + 10.90909091 = 0.00000000
0.00000000 + -4.363636364r + r2 = 0 + 10.90909091
-4.363636364r + r2 = 0 + 10.90909091

Combine like terms: 0 + 10.90909091 = 10.90909091
-4.363636364r + r2 = 10.90909091

The r term is -4.363636364r.  Take half its coefficient (-2.181818182).
Square it (4.760330579) and add it to both sides.

Add '4.760330579' to each side of the equation.
-4.363636364r + 4.760330579 + r2 = 10.90909091 + 4.760330579

Reorder the terms:
4.760330579 + -4.363636364r + r2 = 10.90909091 + 4.760330579

Combine like terms: 10.90909091 + 4.760330579 = 15.669421489
4.760330579 + -4.363636364r + r2 = 15.669421489

Factor a perfect square on the left side:
(r + -2.181818182)(r + -2.181818182) = 15.669421489

Calculate the square root of the right side: 3.958462011

Break this problem into two subproblems by setting 
(r + -2.181818182) equal to 3.958462011 and -3.958462011.

Subproblem 1

r + -2.181818182 = 3.958462011 Simplifying r + -2.181818182 = 3.958462011 Reorder the terms: -2.181818182 + r = 3.958462011 Solving -2.181818182 + r = 3.958462011 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.181818182' to each side of the equation. -2.181818182 + 2.181818182 + r = 3.958462011 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + r = 3.958462011 + 2.181818182 r = 3.958462011 + 2.181818182 Combine like terms: 3.958462011 + 2.181818182 = 6.140280193 r = 6.140280193 Simplifying r = 6.140280193

Subproblem 2

r + -2.181818182 = -3.958462011 Simplifying r + -2.181818182 = -3.958462011 Reorder the terms: -2.181818182 + r = -3.958462011 Solving -2.181818182 + r = -3.958462011 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.181818182' to each side of the equation. -2.181818182 + 2.181818182 + r = -3.958462011 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + r = -3.958462011 + 2.181818182 r = -3.958462011 + 2.181818182 Combine like terms: -3.958462011 + 2.181818182 = -1.776643829 r = -1.776643829 Simplifying r = -1.776643829

Solution

The solution to the problem is based on the solutions from the subproblems. r = {6.140280193, -1.776643829}

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