4.9t^2+26t+0.25=0

Solution for 4.9t^2+26t+0.25=0 equation:

Simplifying
4.9t2 + 26t + 0.25 = 0

Reorder the terms:
0.25 + 26t + 4.9t2 = 0

Solving
0.25 + 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 + 5.306122449t + t2 = 0

Move the constant term to the right:

Add '-0.05102040816' to each side of the equation.
0.05102040816 + 5.306122449t + -0.05102040816 + t2 = 0 + -0.05102040816

Reorder the terms:
0.05102040816 + -0.05102040816 + 5.306122449t + t2 = 0 + -0.05102040816

Combine like terms: 0.05102040816 + -0.05102040816 = 0.00000000000
0.00000000000 + 5.306122449t + t2 = 0 + -0.05102040816
5.306122449t + t2 = 0 + -0.05102040816

Combine like terms: 0 + -0.05102040816 = -0.05102040816
5.306122449t + t2 = -0.05102040816

The t term is 5.306122449t.  Take half its coefficient (2.653061225).
Square it (7.038733864) and add it to both sides.

Add '7.038733864' to each side of the equation.
5.306122449t + 7.038733864 + t2 = -0.05102040816 + 7.038733864

Reorder the terms:
7.038733864 + 5.306122449t + t2 = -0.05102040816 + 7.038733864

Combine like terms: -0.05102040816 + 7.038733864 = 6.98771345584
7.038733864 + 5.306122449t + t2 = 6.98771345584

Factor a perfect square on the left side:
(t + 2.653061225)(t + 2.653061225) = 6.98771345584

Calculate the square root of the right side: 2.643428353

Break this problem into two subproblems by setting 
(t + 2.653061225) equal to 2.643428353 and -2.643428353.

Subproblem 1
t + 2.653061225 = 2.643428353

Simplifying
t + 2.653061225 = 2.643428353

Reorder the terms:
2.653061225 + t = 2.643428353

Solving
2.653061225 + t = 2.643428353

Solving for variable 't'.

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

Add '-2.653061225' to each side of the equation.
2.653061225 + -2.653061225 + t = 2.643428353 + -2.653061225

Combine like terms: 2.653061225 + -2.653061225 = 0.000000000
0.000000000 + t = 2.643428353 + -2.653061225
t = 2.643428353 + -2.653061225

Combine like terms: 2.643428353 + -2.653061225 = -0.009632872
t = -0.009632872

Simplifying
t = -0.009632872

Subproblem 2
t + 2.653061225 = -2.643428353

Simplifying
t + 2.653061225 = -2.643428353

Reorder the terms:
2.653061225 + t = -2.643428353

Solving
2.653061225 + t = -2.643428353

Solving for variable 't'.

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

Add '-2.653061225' to each side of the equation.
2.653061225 + -2.653061225 + t = -2.643428353 + -2.653061225

Combine like terms: 2.653061225 + -2.653061225 = 0.000000000
0.000000000 + t = -2.643428353 + -2.653061225
t = -2.643428353 + -2.653061225

Combine like terms: -2.643428353 + -2.653061225 = -5.296489578
t = -5.296489578

Simplifying
t = -5.296489578

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.009632872, -5.296489578}