4.9t^2+20t-100=0

Solution for 4.9t^2+20t-100=0 equation:

Simplifying
4.9t2 + 20t + -100 = 0

Reorder the terms:
-100 + 20t + 4.9t2 = 0

Solving
-100 + 20t + 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'.
-20.40816327 + 4.081632653t + t2 = 0

Move the constant term to the right:

Add '20.40816327' to each side of the equation.
-20.40816327 + 4.081632653t + 20.40816327 + t2 = 0 + 20.40816327

Reorder the terms:
-20.40816327 + 20.40816327 + 4.081632653t + t2 = 0 + 20.40816327

Combine like terms: -20.40816327 + 20.40816327 = 0.00000000
0.00000000 + 4.081632653t + t2 = 0 + 20.40816327
4.081632653t + t2 = 0 + 20.40816327

Combine like terms: 0 + 20.40816327 = 20.40816327
4.081632653t + t2 = 20.40816327

The t term is 4.081632653t.  Take half its coefficient (2.040816327).
Square it (4.164931281) and add it to both sides.

Add '4.164931281' to each side of the equation.
4.081632653t + 4.164931281 + t2 = 20.40816327 + 4.164931281

Reorder the terms:
4.164931281 + 4.081632653t + t2 = 20.40816327 + 4.164931281

Combine like terms: 20.40816327 + 4.164931281 = 24.573094551
4.164931281 + 4.081632653t + t2 = 24.573094551

Factor a perfect square on the left side:
(t + 2.040816327)(t + 2.040816327) = 24.573094551

Calculate the square root of the right side: 4.957125634

Break this problem into two subproblems by setting 
(t + 2.040816327) equal to 4.957125634 and -4.957125634.

Subproblem 1
t + 2.040816327 = 4.957125634

Simplifying
t + 2.040816327 = 4.957125634

Reorder the terms:
2.040816327 + t = 4.957125634

Solving
2.040816327 + t = 4.957125634

Solving for variable 't'.

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

Add '-2.040816327' to each side of the equation.
2.040816327 + -2.040816327 + t = 4.957125634 + -2.040816327

Combine like terms: 2.040816327 + -2.040816327 = 0.000000000
0.000000000 + t = 4.957125634 + -2.040816327
t = 4.957125634 + -2.040816327

Combine like terms: 4.957125634 + -2.040816327 = 2.916309307
t = 2.916309307

Simplifying
t = 2.916309307

Subproblem 2
t + 2.040816327 = -4.957125634

Simplifying
t + 2.040816327 = -4.957125634

Reorder the terms:
2.040816327 + t = -4.957125634

Solving
2.040816327 + t = -4.957125634

Solving for variable 't'.

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

Add '-2.040816327' to each side of the equation.
2.040816327 + -2.040816327 + t = -4.957125634 + -2.040816327

Combine like terms: 2.040816327 + -2.040816327 = 0.000000000
0.000000000 + t = -4.957125634 + -2.040816327
t = -4.957125634 + -2.040816327

Combine like terms: -4.957125634 + -2.040816327 = -6.997941961
t = -6.997941961

Simplifying
t = -6.997941961

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.916309307, -6.997941961}