2.4r^2-280r-34560=0

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Solution for 2.4r^2-280r-34560=0 equation: 


Simplifying
2.4r2 + -280r + -34560 = 0

Reorder the terms:
-34560 + -280r + 2.4r2 = 0

Solving
-34560 + -280r + 2.4r2 = 0

Solving for variable 'r'.

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

Divide each side by '2.4'.
-14400 + -116.6666667r + r2 = 0

Move the constant term to the right:

Add '14400' to each side of the equation.
-14400 + -116.6666667r + 14400 + r2 = 0 + 14400

Reorder the terms:
-14400 + 14400 + -116.6666667r + r2 = 0 + 14400

Combine like terms: -14400 + 14400 = 0
0 + -116.6666667r + r2 = 0 + 14400
-116.6666667r + r2 = 0 + 14400

Combine like terms: 0 + 14400 = 14400
-116.6666667r + r2 = 14400

The r term is -116.6666667r.  Take half its coefficient (-58.33333335).
Square it (3402.777780) and add it to both sides.

Add '3402.777780' to each side of the equation.
-116.6666667r + 3402.777780 + r2 = 14400 + 3402.777780

Reorder the terms:
3402.777780 + -116.6666667r + r2 = 14400 + 3402.777780

Combine like terms: 14400 + 3402.777780 = 17802.77778
3402.777780 + -116.6666667r + r2 = 17802.77778

Factor a perfect square on the left side:
(r + -58.33333335)(r + -58.33333335) = 17802.77778

Calculate the square root of the right side: 133.427050406

Break this problem into two subproblems by setting 
(r + -58.33333335) equal to 133.427050406 and -133.427050406.


Subproblem 1
r + -58.33333335 = 133.427050406

Simplifying
r + -58.33333335 = 133.427050406

Reorder the terms:
-58.33333335 + r = 133.427050406

Solving
-58.33333335 + r = 133.427050406

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '58.33333335' to each side of the equation.
-58.33333335 + 58.33333335 + r = 133.427050406 + 58.33333335

Combine like terms: -58.33333335 + 58.33333335 = 0.00000000
0.00000000 + r = 133.427050406 + 58.33333335
r = 133.427050406 + 58.33333335

Combine like terms: 133.427050406 + 58.33333335 = 191.760383756
r = 191.760383756

Simplifying
r = 191.760383756


Subproblem 2
r + -58.33333335 = -133.427050406

Simplifying
r + -58.33333335 = -133.427050406

Reorder the terms:
-58.33333335 + r = -133.427050406

Solving
-58.33333335 + r = -133.427050406

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '58.33333335' to each side of the equation.
-58.33333335 + 58.33333335 + r = -133.427050406 + 58.33333335

Combine like terms: -58.33333335 + 58.33333335 = 0.00000000
0.00000000 + r = -133.427050406 + 58.33333335
r = -133.427050406 + 58.33333335

Combine like terms: -133.427050406 + 58.33333335 = -75.093717056
r = -75.093717056

Simplifying
r = -75.093717056


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {191.760383756, -75.093717056}

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