2t+6t^2-9=

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Solution for 2t+6t^2-9= equation: 


Simplifying
2t + 6t2 + -9 = 0

Reorder the terms:
-9 + 2t + 6t2 = 0

Solving
-9 + 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'.
-1.5 + 0.3333333333t + t2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.3333333333t + 1.5 + t2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.3333333333t + t2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.3333333333t + t2 = 0 + 1.5
0.3333333333t + t2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.3333333333t + t2 = 1.5

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 = 1.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333t + t2 = 1.5 + 0.02777777779

Combine like terms: 1.5 + 0.02777777779 = 1.52777777779
0.02777777779 + 0.3333333333t + t2 = 1.52777777779

Factor a perfect square on the left side:
(t + 0.1666666667)(t + 0.1666666667) = 1.52777777779

Calculate the square root of the right side: 1.236033081

Break this problem into two subproblems by setting 
(t + 0.1666666667) equal to 1.236033081 and -1.236033081.


Subproblem 1
t + 0.1666666667 = 1.236033081

Simplifying
t + 0.1666666667 = 1.236033081

Reorder the terms:
0.1666666667 + t = 1.236033081

Solving
0.1666666667 + t = 1.236033081

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 = 1.236033081 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + t = 1.236033081 + -0.1666666667
t = 1.236033081 + -0.1666666667

Combine like terms: 1.236033081 + -0.1666666667 = 1.0693664143
t = 1.0693664143

Simplifying
t = 1.0693664143


Subproblem 2
t + 0.1666666667 = -1.236033081

Simplifying
t + 0.1666666667 = -1.236033081

Reorder the terms:
0.1666666667 + t = -1.236033081

Solving
0.1666666667 + t = -1.236033081

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 = -1.236033081 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + t = -1.236033081 + -0.1666666667
t = -1.236033081 + -0.1666666667

Combine like terms: -1.236033081 + -0.1666666667 = -1.4026997477
t = -1.4026997477

Simplifying
t = -1.4026997477


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.0693664143, -1.4026997477}

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