4.9t^2-30t-40=0

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Solution for 4.9t^2-30t-40=0 equation: 


Simplifying
4.9t2 + -30t + -40 = 0

Reorder the terms:
-40 + -30t + 4.9t2 = 0

Solving
-40 + -30t + 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'.
-8.163265306 + -6.12244898t + t2 = 0

Move the constant term to the right:

Add '8.163265306' to each side of the equation.
-8.163265306 + -6.12244898t + 8.163265306 + t2 = 0 + 8.163265306

Reorder the terms:
-8.163265306 + 8.163265306 + -6.12244898t + t2 = 0 + 8.163265306

Combine like terms: -8.163265306 + 8.163265306 = 0.000000000
0.000000000 + -6.12244898t + t2 = 0 + 8.163265306
-6.12244898t + t2 = 0 + 8.163265306

Combine like terms: 0 + 8.163265306 = 8.163265306
-6.12244898t + t2 = 8.163265306

The t term is -6.12244898t.  Take half its coefficient (-3.06122449).
Square it (9.371095378) and add it to both sides.

Add '9.371095378' to each side of the equation.
-6.12244898t + 9.371095378 + t2 = 8.163265306 + 9.371095378

Reorder the terms:
9.371095378 + -6.12244898t + t2 = 8.163265306 + 9.371095378

Combine like terms: 8.163265306 + 9.371095378 = 17.534360684
9.371095378 + -6.12244898t + t2 = 17.534360684

Factor a perfect square on the left side:
(t + -3.06122449)(t + -3.06122449) = 17.534360684

Calculate the square root of the right side: 4.187405006

Break this problem into two subproblems by setting 
(t + -3.06122449) equal to 4.187405006 and -4.187405006.


Subproblem 1
t + -3.06122449 = 4.187405006

Simplifying
t + -3.06122449 = 4.187405006

Reorder the terms:
-3.06122449 + t = 4.187405006

Solving
-3.06122449 + t = 4.187405006

Solving for variable 't'.

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

Add '3.06122449' to each side of the equation.
-3.06122449 + 3.06122449 + t = 4.187405006 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + t = 4.187405006 + 3.06122449
t = 4.187405006 + 3.06122449

Combine like terms: 4.187405006 + 3.06122449 = 7.248629496
t = 7.248629496

Simplifying
t = 7.248629496


Subproblem 2
t + -3.06122449 = -4.187405006

Simplifying
t + -3.06122449 = -4.187405006

Reorder the terms:
-3.06122449 + t = -4.187405006

Solving
-3.06122449 + t = -4.187405006

Solving for variable 't'.

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

Add '3.06122449' to each side of the equation.
-3.06122449 + 3.06122449 + t = -4.187405006 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + t = -4.187405006 + 3.06122449
t = -4.187405006 + 3.06122449

Combine like terms: -4.187405006 + 3.06122449 = -1.126180516
t = -1.126180516

Simplifying
t = -1.126180516


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.248629496, -1.126180516}

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