49t^2+360t-2160=0

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Solution for 49t^2+360t-2160=0 equation: 


Simplifying
49t2 + 360t + -2160 = 0

Reorder the terms:
-2160 + 360t + 49t2 = 0

Solving
-2160 + 360t + 49t2 = 0

Solving for variable 't'.

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

Divide each side by '49'.
-44.08163265 + 7.346938776t + t2 = 0

Move the constant term to the right:

Add '44.08163265' to each side of the equation.
-44.08163265 + 7.346938776t + 44.08163265 + t2 = 0 + 44.08163265

Reorder the terms:
-44.08163265 + 44.08163265 + 7.346938776t + t2 = 0 + 44.08163265

Combine like terms: -44.08163265 + 44.08163265 = 0.00000000
0.00000000 + 7.346938776t + t2 = 0 + 44.08163265
7.346938776t + t2 = 0 + 44.08163265

Combine like terms: 0 + 44.08163265 = 44.08163265
7.346938776t + t2 = 44.08163265

The t term is 7.346938776t.  Take half its coefficient (3.673469388).
Square it (13.49437734) and add it to both sides.

Add '13.49437734' to each side of the equation.
7.346938776t + 13.49437734 + t2 = 44.08163265 + 13.49437734

Reorder the terms:
13.49437734 + 7.346938776t + t2 = 44.08163265 + 13.49437734

Combine like terms: 44.08163265 + 13.49437734 = 57.57600999
13.49437734 + 7.346938776t + t2 = 57.57600999

Factor a perfect square on the left side:
(t + 3.673469388)(t + 3.673469388) = 57.57600999

Calculate the square root of the right side: 7.587885739

Break this problem into two subproblems by setting 
(t + 3.673469388) equal to 7.587885739 and -7.587885739.


Subproblem 1
t + 3.673469388 = 7.587885739

Simplifying
t + 3.673469388 = 7.587885739

Reorder the terms:
3.673469388 + t = 7.587885739

Solving
3.673469388 + t = 7.587885739

Solving for variable 't'.

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

Add '-3.673469388' to each side of the equation.
3.673469388 + -3.673469388 + t = 7.587885739 + -3.673469388

Combine like terms: 3.673469388 + -3.673469388 = 0.000000000
0.000000000 + t = 7.587885739 + -3.673469388
t = 7.587885739 + -3.673469388

Combine like terms: 7.587885739 + -3.673469388 = 3.914416351
t = 3.914416351

Simplifying
t = 3.914416351


Subproblem 2
t + 3.673469388 = -7.587885739

Simplifying
t + 3.673469388 = -7.587885739

Reorder the terms:
3.673469388 + t = -7.587885739

Solving
3.673469388 + t = -7.587885739

Solving for variable 't'.

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

Add '-3.673469388' to each side of the equation.
3.673469388 + -3.673469388 + t = -7.587885739 + -3.673469388

Combine like terms: 3.673469388 + -3.673469388 = 0.000000000
0.000000000 + t = -7.587885739 + -3.673469388
t = -7.587885739 + -3.673469388

Combine like terms: -7.587885739 + -3.673469388 = -11.261355127
t = -11.261355127

Simplifying
t = -11.261355127


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.914416351, -11.261355127}

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