4.9t^2+38t-240=0

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Solution for 4.9t^2+38t-240=0 equation: 


Simplifying
4.9t2 + 38t + -240 = 0

Reorder the terms:
-240 + 38t + 4.9t2 = 0

Solving
-240 + 38t + 4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '4.9'.
-48.97959184 + 7.755102041t + t2 = 0

Move the constant term to the right:

Add '48.97959184' to each side of the equation.
-48.97959184 + 7.755102041t + 48.97959184 + t2 = 0 + 48.97959184

Reorder the terms:
-48.97959184 + 48.97959184 + 7.755102041t + t2 = 0 + 48.97959184

Combine like terms: -48.97959184 + 48.97959184 = 0.00000000
0.00000000 + 7.755102041t + t2 = 0 + 48.97959184
7.755102041t + t2 = 0 + 48.97959184

Combine like terms: 0 + 48.97959184 = 48.97959184
7.755102041t + t2 = 48.97959184

The t term is 7.755102041t.  Take half its coefficient (3.877551021).
Square it (15.03540192) and add it to both sides.

Add '15.03540192' to each side of the equation.
7.755102041t + 15.03540192 + t2 = 48.97959184 + 15.03540192

Reorder the terms:
15.03540192 + 7.755102041t + t2 = 48.97959184 + 15.03540192

Combine like terms: 48.97959184 + 15.03540192 = 64.01499376
15.03540192 + 7.755102041t + t2 = 64.01499376

Factor a perfect square on the left side:
(t + 3.877551021)(t + 3.877551021) = 64.01499376

Calculate the square root of the right side: 8.000937055

Break this problem into two subproblems by setting 
(t + 3.877551021) equal to 8.000937055 and -8.000937055.


Subproblem 1
t + 3.877551021 = 8.000937055

Simplifying
t + 3.877551021 = 8.000937055

Reorder the terms:
3.877551021 + t = 8.000937055

Solving
3.877551021 + t = 8.000937055

Solving for variable 't'.

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

Add '-3.877551021' to each side of the equation.
3.877551021 + -3.877551021 + t = 8.000937055 + -3.877551021

Combine like terms: 3.877551021 + -3.877551021 = 0.000000000
0.000000000 + t = 8.000937055 + -3.877551021
t = 8.000937055 + -3.877551021

Combine like terms: 8.000937055 + -3.877551021 = 4.123386034
t = 4.123386034

Simplifying
t = 4.123386034


Subproblem 2
t + 3.877551021 = -8.000937055

Simplifying
t + 3.877551021 = -8.000937055

Reorder the terms:
3.877551021 + t = -8.000937055

Solving
3.877551021 + t = -8.000937055

Solving for variable 't'.

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

Add '-3.877551021' to each side of the equation.
3.877551021 + -3.877551021 + t = -8.000937055 + -3.877551021

Combine like terms: 3.877551021 + -3.877551021 = 0.000000000
0.000000000 + t = -8.000937055 + -3.877551021
t = -8.000937055 + -3.877551021

Combine like terms: -8.000937055 + -3.877551021 = -11.878488076
t = -11.878488076

Simplifying
t = -11.878488076


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.123386034, -11.878488076}

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