-4.9t^2+30.5t+8.7=0

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Solution for -4.9t^2+30.5t+8.7=0 equation: 


Simplifying
-4.9t2 + 30.5t + 8.7 = 0

Reorder the terms:
8.7 + 30.5t + -4.9t2 = 0

Solving
8.7 + 30.5t + -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'.
-1.775510204 + -6.224489796t + t2 = 0

Move the constant term to the right:

Add '1.775510204' to each side of the equation.
-1.775510204 + -6.224489796t + 1.775510204 + t2 = 0 + 1.775510204

Reorder the terms:
-1.775510204 + 1.775510204 + -6.224489796t + t2 = 0 + 1.775510204

Combine like terms: -1.775510204 + 1.775510204 = 0.000000000
0.000000000 + -6.224489796t + t2 = 0 + 1.775510204
-6.224489796t + t2 = 0 + 1.775510204

Combine like terms: 0 + 1.775510204 = 1.775510204
-6.224489796t + t2 = 1.775510204

The t term is -6.224489796t.  Take half its coefficient (-3.112244898).
Square it (9.686068305) and add it to both sides.

Add '9.686068305' to each side of the equation.
-6.224489796t + 9.686068305 + t2 = 1.775510204 + 9.686068305

Reorder the terms:
9.686068305 + -6.224489796t + t2 = 1.775510204 + 9.686068305

Combine like terms: 1.775510204 + 9.686068305 = 11.461578509
9.686068305 + -6.224489796t + t2 = 11.461578509

Factor a perfect square on the left side:
(t + -3.112244898)(t + -3.112244898) = 11.461578509

Calculate the square root of the right side: 3.385495312

Break this problem into two subproblems by setting 
(t + -3.112244898) equal to 3.385495312 and -3.385495312.


Subproblem 1
t + -3.112244898 = 3.385495312

Simplifying
t + -3.112244898 = 3.385495312

Reorder the terms:
-3.112244898 + t = 3.385495312

Solving
-3.112244898 + t = 3.385495312

Solving for variable 't'.

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

Add '3.112244898' to each side of the equation.
-3.112244898 + 3.112244898 + t = 3.385495312 + 3.112244898

Combine like terms: -3.112244898 + 3.112244898 = 0.000000000
0.000000000 + t = 3.385495312 + 3.112244898
t = 3.385495312 + 3.112244898

Combine like terms: 3.385495312 + 3.112244898 = 6.49774021
t = 6.49774021

Simplifying
t = 6.49774021


Subproblem 2
t + -3.112244898 = -3.385495312

Simplifying
t + -3.112244898 = -3.385495312

Reorder the terms:
-3.112244898 + t = -3.385495312

Solving
-3.112244898 + t = -3.385495312

Solving for variable 't'.

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

Add '3.112244898' to each side of the equation.
-3.112244898 + 3.112244898 + t = -3.385495312 + 3.112244898

Combine like terms: -3.112244898 + 3.112244898 = 0.000000000
0.000000000 + t = -3.385495312 + 3.112244898
t = -3.385495312 + 3.112244898

Combine like terms: -3.385495312 + 3.112244898 = -0.273250414
t = -0.273250414

Simplifying
t = -0.273250414


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.49774021, -0.273250414}

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