40t^2-98t-245=0

Solution for 40t^2-98t-245=0 equation:

Simplifying
40t2 + -98t + -245 = 0

Reorder the terms:
-245 + -98t + 40t2 = 0

Solving
-245 + -98t + 40t2 = 0

Solving for variable 't'.

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

Divide each side by '40'.
-6.125 + -2.45t + t2 = 0

Move the constant term to the right:

Add '6.125' to each side of the equation.
-6.125 + -2.45t + 6.125 + t2 = 0 + 6.125

Reorder the terms:
-6.125 + 6.125 + -2.45t + t2 = 0 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + -2.45t + t2 = 0 + 6.125
-2.45t + t2 = 0 + 6.125

Combine like terms: 0 + 6.125 = 6.125
-2.45t + t2 = 6.125

The t term is -2.45t.  Take half its coefficient (-1.225).
Square it (1.500625) and add it to both sides.

Add '1.500625' to each side of the equation.
-2.45t + 1.500625 + t2 = 6.125 + 1.500625

Reorder the terms:
1.500625 + -2.45t + t2 = 6.125 + 1.500625

Combine like terms: 6.125 + 1.500625 = 7.625625
1.500625 + -2.45t + t2 = 7.625625

Factor a perfect square on the left side:
(t + -1.225)(t + -1.225) = 7.625625

Calculate the square root of the right side: 2.761453422

Break this problem into two subproblems by setting 
(t + -1.225) equal to 2.761453422 and -2.761453422.

Subproblem 1
t + -1.225 = 2.761453422

Simplifying
t + -1.225 = 2.761453422

Reorder the terms:
-1.225 + t = 2.761453422

Solving
-1.225 + t = 2.761453422

Solving for variable 't'.

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

Add '1.225' to each side of the equation.
-1.225 + 1.225 + t = 2.761453422 + 1.225

Combine like terms: -1.225 + 1.225 = 0.000
0.000 + t = 2.761453422 + 1.225
t = 2.761453422 + 1.225

Combine like terms: 2.761453422 + 1.225 = 3.986453422
t = 3.986453422

Simplifying
t = 3.986453422

Subproblem 2
t + -1.225 = -2.761453422

Simplifying
t + -1.225 = -2.761453422

Reorder the terms:
-1.225 + t = -2.761453422

Solving
-1.225 + t = -2.761453422

Solving for variable 't'.

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

Add '1.225' to each side of the equation.
-1.225 + 1.225 + t = -2.761453422 + 1.225

Combine like terms: -1.225 + 1.225 = 0.000
0.000 + t = -2.761453422 + 1.225
t = -2.761453422 + 1.225

Combine like terms: -2.761453422 + 1.225 = -1.536453422
t = -1.536453422

Simplifying
t = -1.536453422

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.986453422, -1.536453422}