3t^2-8t-8=15

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Solution for 3t^2-8t-8=15 equation: 


Simplifying
3t2 + -8t + -8 = 15

Reorder the terms:
-8 + -8t + 3t2 = 15

Solving
-8 + -8t + 3t2 = 15

Solving for variable 't'.

Reorder the terms:
-8 + -15 + -8t + 3t2 = 15 + -15

Combine like terms: -8 + -15 = -23
-23 + -8t + 3t2 = 15 + -15

Combine like terms: 15 + -15 = 0
-23 + -8t + 3t2 = 0

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

Divide each side by '3'.
-7.666666667 + -2.666666667t + t2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + -2.666666667t + 7.666666667 + t2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + -2.666666667t + t2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + -2.666666667t + t2 = 0 + 7.666666667
-2.666666667t + t2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
-2.666666667t + t2 = 7.666666667

The t term is -2.666666667t.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667t + 1.777777780 + t2 = 7.666666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667t + t2 = 7.666666667 + 1.777777780

Combine like terms: 7.666666667 + 1.777777780 = 9.444444447
1.777777780 + -2.666666667t + t2 = 9.444444447

Factor a perfect square on the left side:
(t + -1.333333334)(t + -1.333333334) = 9.444444447

Calculate the square root of the right side: 3.073181486

Break this problem into two subproblems by setting 
(t + -1.333333334) equal to 3.073181486 and -3.073181486.


Subproblem 1
t + -1.333333334 = 3.073181486

Simplifying
t + -1.333333334 = 3.073181486

Reorder the terms:
-1.333333334 + t = 3.073181486

Solving
-1.333333334 + t = 3.073181486

Solving for variable 't'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + t = 3.073181486 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + t = 3.073181486 + 1.333333334
t = 3.073181486 + 1.333333334

Combine like terms: 3.073181486 + 1.333333334 = 4.40651482
t = 4.40651482

Simplifying
t = 4.40651482


Subproblem 2
t + -1.333333334 = -3.073181486

Simplifying
t + -1.333333334 = -3.073181486

Reorder the terms:
-1.333333334 + t = -3.073181486

Solving
-1.333333334 + t = -3.073181486

Solving for variable 't'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + t = -3.073181486 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + t = -3.073181486 + 1.333333334
t = -3.073181486 + 1.333333334

Combine like terms: -3.073181486 + 1.333333334 = -1.739848152
t = -1.739848152

Simplifying
t = -1.739848152


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.40651482, -1.739848152}

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