6t^2+2t-99=0

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Solution for 6t^2+2t-99=0 equation: 


Simplifying
6t2 + 2t + -99 = 0

Reorder the terms:
-99 + 2t + 6t2 = 0

Solving
-99 + 2t + 6t2 = 0

Solving for variable 't'.

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

Divide each side by '6'.
-16.5 + 0.3333333333t + t2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + 0.3333333333t + 16.5 + t2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + 0.3333333333t + t2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + 0.3333333333t + t2 = 0 + 16.5
0.3333333333t + t2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
0.3333333333t + t2 = 16.5

The t term is 0.3333333333t.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333t + 0.02777777779 + t2 = 16.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333t + t2 = 16.5 + 0.02777777779

Combine like terms: 16.5 + 0.02777777779 = 16.52777777779
0.02777777779 + 0.3333333333t + t2 = 16.52777777779

Factor a perfect square on the left side:
(t + 0.1666666667)(t + 0.1666666667) = 16.52777777779

Calculate the square root of the right side: 4.065436973

Break this problem into two subproblems by setting 
(t + 0.1666666667) equal to 4.065436973 and -4.065436973.


Subproblem 1
t + 0.1666666667 = 4.065436973

Simplifying
t + 0.1666666667 = 4.065436973

Reorder the terms:
0.1666666667 + t = 4.065436973

Solving
0.1666666667 + t = 4.065436973

Solving for variable 't'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + t = 4.065436973 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + t = 4.065436973 + -0.1666666667
t = 4.065436973 + -0.1666666667

Combine like terms: 4.065436973 + -0.1666666667 = 3.8987703063
t = 3.8987703063

Simplifying
t = 3.8987703063


Subproblem 2
t + 0.1666666667 = -4.065436973

Simplifying
t + 0.1666666667 = -4.065436973

Reorder the terms:
0.1666666667 + t = -4.065436973

Solving
0.1666666667 + t = -4.065436973

Solving for variable 't'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + t = -4.065436973 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + t = -4.065436973 + -0.1666666667
t = -4.065436973 + -0.1666666667

Combine like terms: -4.065436973 + -0.1666666667 = -4.2321036397
t = -4.2321036397

Simplifying
t = -4.2321036397


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.8987703063, -4.2321036397}

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