-2.7t^2+40t+6.5=

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Solution for -2.7t^2+40t+6.5= equation: 


Simplifying
-2.7t2 + 40t + 6.5 = 0

Reorder the terms:
6.5 + 40t + -2.7t2 = 0

Solving
6.5 + 40t + -2.7t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-2.7 the coefficient of the squared term: 

Divide each side by '-2.7'.
-2.407407407 + -14.81481481t + t2 = 0

Move the constant term to the right:

Add '2.407407407' to each side of the equation.
-2.407407407 + -14.81481481t + 2.407407407 + t2 = 0 + 2.407407407

Reorder the terms:
-2.407407407 + 2.407407407 + -14.81481481t + t2 = 0 + 2.407407407

Combine like terms: -2.407407407 + 2.407407407 = 0.000000000
0.000000000 + -14.81481481t + t2 = 0 + 2.407407407
-14.81481481t + t2 = 0 + 2.407407407

Combine like terms: 0 + 2.407407407 = 2.407407407
-14.81481481t + t2 = 2.407407407

The t term is -14.81481481t.  Take half its coefficient (-7.407407405).
Square it (54.86968446) and add it to both sides.

Add '54.86968446' to each side of the equation.
-14.81481481t + 54.86968446 + t2 = 2.407407407 + 54.86968446

Reorder the terms:
54.86968446 + -14.81481481t + t2 = 2.407407407 + 54.86968446

Combine like terms: 2.407407407 + 54.86968446 = 57.277091867
54.86968446 + -14.81481481t + t2 = 57.277091867

Factor a perfect square on the left side:
(t + -7.407407405)(t + -7.407407405) = 57.277091867

Calculate the square root of the right side: 7.568163044

Break this problem into two subproblems by setting 
(t + -7.407407405) equal to 7.568163044 and -7.568163044.


Subproblem 1
t + -7.407407405 = 7.568163044

Simplifying
t + -7.407407405 = 7.568163044

Reorder the terms:
-7.407407405 + t = 7.568163044

Solving
-7.407407405 + t = 7.568163044

Solving for variable 't'.

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

Add '7.407407405' to each side of the equation.
-7.407407405 + 7.407407405 + t = 7.568163044 + 7.407407405

Combine like terms: -7.407407405 + 7.407407405 = 0.000000000
0.000000000 + t = 7.568163044 + 7.407407405
t = 7.568163044 + 7.407407405

Combine like terms: 7.568163044 + 7.407407405 = 14.975570449
t = 14.975570449

Simplifying
t = 14.975570449


Subproblem 2
t + -7.407407405 = -7.568163044

Simplifying
t + -7.407407405 = -7.568163044

Reorder the terms:
-7.407407405 + t = -7.568163044

Solving
-7.407407405 + t = -7.568163044

Solving for variable 't'.

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

Add '7.407407405' to each side of the equation.
-7.407407405 + 7.407407405 + t = -7.568163044 + 7.407407405

Combine like terms: -7.407407405 + 7.407407405 = 0.000000000
0.000000000 + t = -7.568163044 + 7.407407405
t = -7.568163044 + 7.407407405

Combine like terms: -7.568163044 + 7.407407405 = -0.160755639
t = -0.160755639

Simplifying
t = -0.160755639


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.975570449, -0.160755639}

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