4.9t^2-1.26t-0.25=0

Solution for 4.9t^2-1.26t-0.25=0 equation:

Simplifying
4.9t2 + -1.26t + -0.25 = 0

Reorder the terms:
-0.25 + -1.26t + 4.9t2 = 0

Solving
-0.25 + -1.26t + 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'.
-0.05102040816 + -0.2571428571t + t2 = 0

Move the constant term to the right:

Add '0.05102040816' to each side of the equation.
-0.05102040816 + -0.2571428571t + 0.05102040816 + t2 = 0 + 0.05102040816

Reorder the terms:
-0.05102040816 + 0.05102040816 + -0.2571428571t + t2 = 0 + 0.05102040816

Combine like terms: -0.05102040816 + 0.05102040816 = 0.00000000000
0.00000000000 + -0.2571428571t + t2 = 0 + 0.05102040816
-0.2571428571t + t2 = 0 + 0.05102040816

Combine like terms: 0 + 0.05102040816 = 0.05102040816
-0.2571428571t + t2 = 0.05102040816

The t term is -0.2571428571t.  Take half its coefficient (-0.1285714286).
Square it (0.01653061225) and add it to both sides.

Add '0.01653061225' to each side of the equation.
-0.2571428571t + 0.01653061225 + t2 = 0.05102040816 + 0.01653061225

Reorder the terms:
0.01653061225 + -0.2571428571t + t2 = 0.05102040816 + 0.01653061225

Combine like terms: 0.05102040816 + 0.01653061225 = 0.06755102041
0.01653061225 + -0.2571428571t + t2 = 0.06755102041

Factor a perfect square on the left side:
(t + -0.1285714286)(t + -0.1285714286) = 0.06755102041

Calculate the square root of the right side: 0.259905791

Break this problem into two subproblems by setting 
(t + -0.1285714286) equal to 0.259905791 and -0.259905791.

Subproblem 1
t + -0.1285714286 = 0.259905791

Simplifying
t + -0.1285714286 = 0.259905791

Reorder the terms:
-0.1285714286 + t = 0.259905791

Solving
-0.1285714286 + t = 0.259905791

Solving for variable 't'.

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

Add '0.1285714286' to each side of the equation.
-0.1285714286 + 0.1285714286 + t = 0.259905791 + 0.1285714286

Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000
0.0000000000 + t = 0.259905791 + 0.1285714286
t = 0.259905791 + 0.1285714286

Combine like terms: 0.259905791 + 0.1285714286 = 0.3884772196
t = 0.3884772196

Simplifying
t = 0.3884772196

Subproblem 2
t + -0.1285714286 = -0.259905791

Simplifying
t + -0.1285714286 = -0.259905791

Reorder the terms:
-0.1285714286 + t = -0.259905791

Solving
-0.1285714286 + t = -0.259905791

Solving for variable 't'.

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

Add '0.1285714286' to each side of the equation.
-0.1285714286 + 0.1285714286 + t = -0.259905791 + 0.1285714286

Combine like terms: -0.1285714286 + 0.1285714286 = 0.0000000000
0.0000000000 + t = -0.259905791 + 0.1285714286
t = -0.259905791 + 0.1285714286

Combine like terms: -0.259905791 + 0.1285714286 = -0.1313343624
t = -0.1313343624

Simplifying
t = -0.1313343624

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.3884772196, -0.1313343624}