4.9t^2+t-55=0

Solution for 4.9t^2+t-55=0 equation:

Simplifying
4.9t2 + t + -55 = 0

Reorder the terms:
-55 + t + 4.9t2 = 0

Solving
-55 + t + 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'.
-11.2244898 + 0.2040816327t + t2 = 0

Move the constant term to the right:

Add '11.2244898' to each side of the equation.
-11.2244898 + 0.2040816327t + 11.2244898 + t2 = 0 + 11.2244898

Reorder the terms:
-11.2244898 + 11.2244898 + 0.2040816327t + t2 = 0 + 11.2244898

Combine like terms: -11.2244898 + 11.2244898 = 0.0000000
0.0000000 + 0.2040816327t + t2 = 0 + 11.2244898
0.2040816327t + t2 = 0 + 11.2244898

Combine like terms: 0 + 11.2244898 = 11.2244898
0.2040816327t + t2 = 11.2244898

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2040816327t + 0.25 + t2 = 11.2244898 + 0.25

Reorder the terms:
0.25 + 0.2040816327t + t2 = 11.2244898 + 0.25

Combine like terms: 11.2244898 + 0.25 = 11.4744898
0.25 + 0.2040816327t + t2 = 11.4744898

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 11.4744898

Calculate the square root of the right side: 3.38740163

Break this problem into two subproblems by setting 
(t + 0.5) equal to 3.38740163 and -3.38740163.

Subproblem 1
t + 0.5 = 3.38740163

Simplifying
t + 0.5 = 3.38740163

Reorder the terms:
0.5 + t = 3.38740163

Solving
0.5 + t = 3.38740163

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 3.38740163 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 3.38740163 + -0.5
t = 3.38740163 + -0.5

Combine like terms: 3.38740163 + -0.5 = 2.88740163
t = 2.88740163

Simplifying
t = 2.88740163

Subproblem 2
t + 0.5 = -3.38740163

Simplifying
t + 0.5 = -3.38740163

Reorder the terms:
0.5 + t = -3.38740163

Solving
0.5 + t = -3.38740163

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -3.38740163 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -3.38740163 + -0.5
t = -3.38740163 + -0.5

Combine like terms: -3.38740163 + -0.5 = -3.88740163
t = -3.88740163

Simplifying
t = -3.88740163

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.88740163, -3.88740163}