0=-4.9t^2+9t+500

Solution for 0=-4.9t^2+9t+500 equation:

Simplifying
0 = -4.9t2 + 9t + 500

Reorder the terms:
0 = 500 + 9t + -4.9t2

Solving
0 = 500 + 9t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -500 = -500
-500 + -9t + 4.9t2 = 500 + 9t + -4.9t2 + -500 + -9t + 4.9t2

Reorder the terms:
-500 + -9t + 4.9t2 = 500 + -500 + 9t + -9t + -4.9t2 + 4.9t2

Combine like terms: 500 + -500 = 0
-500 + -9t + 4.9t2 = 0 + 9t + -9t + -4.9t2 + 4.9t2
-500 + -9t + 4.9t2 = 9t + -9t + -4.9t2 + 4.9t2

Combine like terms: 9t + -9t = 0
-500 + -9t + 4.9t2 = 0 + -4.9t2 + 4.9t2
-500 + -9t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-500 + -9t + 4.9t2 = 0.0

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

Divide each side by '4.9'.
-102.0408163 + -1.836734694t + t2 = 0

Move the constant term to the right:

Add '102.0408163' to each side of the equation.
-102.0408163 + -1.836734694t + 102.0408163 + t2 = 0 + 102.0408163

Reorder the terms:
-102.0408163 + 102.0408163 + -1.836734694t + t2 = 0 + 102.0408163

Combine like terms: -102.0408163 + 102.0408163 = 0.0000000
0.0000000 + -1.836734694t + t2 = 0 + 102.0408163
-1.836734694t + t2 = 0 + 102.0408163

Combine like terms: 0 + 102.0408163 = 102.0408163
-1.836734694t + t2 = 102.0408163

The t term is -1.836734694t.  Take half its coefficient (-0.918367347).
Square it (0.8433985840) and add it to both sides.

Add '0.8433985840' to each side of the equation.
-1.836734694t + 0.8433985840 + t2 = 102.0408163 + 0.8433985840

Reorder the terms:
0.8433985840 + -1.836734694t + t2 = 102.0408163 + 0.8433985840

Combine like terms: 102.0408163 + 0.8433985840 = 102.884214884
0.8433985840 + -1.836734694t + t2 = 102.884214884

Factor a perfect square on the left side:
(t + -0.918367347)(t + -0.918367347) = 102.884214884

Calculate the square root of the right side: 10.143185638

Break this problem into two subproblems by setting 
(t + -0.918367347) equal to 10.143185638 and -10.143185638.

Subproblem 1
t + -0.918367347 = 10.143185638

Simplifying
t + -0.918367347 = 10.143185638

Reorder the terms:
-0.918367347 + t = 10.143185638

Solving
-0.918367347 + t = 10.143185638

Solving for variable 't'.

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

Add '0.918367347' to each side of the equation.
-0.918367347 + 0.918367347 + t = 10.143185638 + 0.918367347

Combine like terms: -0.918367347 + 0.918367347 = 0.000000000
0.000000000 + t = 10.143185638 + 0.918367347
t = 10.143185638 + 0.918367347

Combine like terms: 10.143185638 + 0.918367347 = 11.061552985
t = 11.061552985

Simplifying
t = 11.061552985

Subproblem 2
t + -0.918367347 = -10.143185638

Simplifying
t + -0.918367347 = -10.143185638

Reorder the terms:
-0.918367347 + t = -10.143185638

Solving
-0.918367347 + t = -10.143185638

Solving for variable 't'.

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

Add '0.918367347' to each side of the equation.
-0.918367347 + 0.918367347 + t = -10.143185638 + 0.918367347

Combine like terms: -0.918367347 + 0.918367347 = 0.000000000
0.000000000 + t = -10.143185638 + 0.918367347
t = -10.143185638 + 0.918367347

Combine like terms: -10.143185638 + 0.918367347 = -9.224818291
t = -9.224818291

Simplifying
t = -9.224818291

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.061552985, -9.224818291}