4.9t^2+38t-265=0

Solution for 4.9t^2+38t-265=0 equation:

Simplifying
4.9t2 + 38t + -265 = 0

Reorder the terms:
-265 + 38t + 4.9t2 = 0

Solving
-265 + 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'.
-54.08163265 + 7.755102041t + t2 = 0

Move the constant term to the right:

Add '54.08163265' to each side of the equation.
-54.08163265 + 7.755102041t + 54.08163265 + t2 = 0 + 54.08163265

Reorder the terms:
-54.08163265 + 54.08163265 + 7.755102041t + t2 = 0 + 54.08163265

Combine like terms: -54.08163265 + 54.08163265 = 0.00000000
0.00000000 + 7.755102041t + t2 = 0 + 54.08163265
7.755102041t + t2 = 0 + 54.08163265

Combine like terms: 0 + 54.08163265 = 54.08163265
7.755102041t + t2 = 54.08163265

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 = 54.08163265 + 15.03540192

Reorder the terms:
15.03540192 + 7.755102041t + t2 = 54.08163265 + 15.03540192

Combine like terms: 54.08163265 + 15.03540192 = 69.11703457
15.03540192 + 7.755102041t + t2 = 69.11703457

Factor a perfect square on the left side:
(t + 3.877551021)(t + 3.877551021) = 69.11703457

Calculate the square root of the right side: 8.313665532

Break this problem into two subproblems by setting 
(t + 3.877551021) equal to 8.313665532 and -8.313665532.

Subproblem 1
t + 3.877551021 = 8.313665532

Simplifying
t + 3.877551021 = 8.313665532

Reorder the terms:
3.877551021 + t = 8.313665532

Solving
3.877551021 + t = 8.313665532

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 = 8.313665532 + -3.877551021

Combine like terms: 3.877551021 + -3.877551021 = 0.000000000
0.000000000 + t = 8.313665532 + -3.877551021
t = 8.313665532 + -3.877551021

Combine like terms: 8.313665532 + -3.877551021 = 4.436114511
t = 4.436114511

Simplifying
t = 4.436114511

Subproblem 2
t + 3.877551021 = -8.313665532

Simplifying
t + 3.877551021 = -8.313665532

Reorder the terms:
3.877551021 + t = -8.313665532

Solving
3.877551021 + t = -8.313665532

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 = -8.313665532 + -3.877551021

Combine like terms: 3.877551021 + -3.877551021 = 0.000000000
0.000000000 + t = -8.313665532 + -3.877551021
t = -8.313665532 + -3.877551021

Combine like terms: -8.313665532 + -3.877551021 = -12.191216553
t = -12.191216553

Simplifying
t = -12.191216553

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.436114511, -12.191216553}