-2.7t^2+50t+6.5=0

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Solution for -2.7t^2+50t+6.5=0 equation: 


Simplifying
-2.7t2 + 50t + 6.5 = 0

Reorder the terms:
6.5 + 50t + -2.7t2 = 0

Solving
6.5 + 50t + -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 + -18.51851852t + t2 = 0

Move the constant term to the right:

Add '2.407407407' to each side of the equation.
-2.407407407 + -18.51851852t + 2.407407407 + t2 = 0 + 2.407407407

Reorder the terms:
-2.407407407 + 2.407407407 + -18.51851852t + t2 = 0 + 2.407407407

Combine like terms: -2.407407407 + 2.407407407 = 0.000000000
0.000000000 + -18.51851852t + t2 = 0 + 2.407407407
-18.51851852t + t2 = 0 + 2.407407407

Combine like terms: 0 + 2.407407407 = 2.407407407
-18.51851852t + t2 = 2.407407407

The t term is -18.51851852t.  Take half its coefficient (-9.25925926).
Square it (85.73388204) and add it to both sides.

Add '85.73388204' to each side of the equation.
-18.51851852t + 85.73388204 + t2 = 2.407407407 + 85.73388204

Reorder the terms:
85.73388204 + -18.51851852t + t2 = 2.407407407 + 85.73388204

Combine like terms: 2.407407407 + 85.73388204 = 88.141289447
85.73388204 + -18.51851852t + t2 = 88.141289447

Factor a perfect square on the left side:
(t + -9.25925926)(t + -9.25925926) = 88.141289447

Calculate the square root of the right side: 9.388359252

Break this problem into two subproblems by setting 
(t + -9.25925926) equal to 9.388359252 and -9.388359252.


Subproblem 1
t + -9.25925926 = 9.388359252

Simplifying
t + -9.25925926 = 9.388359252

Reorder the terms:
-9.25925926 + t = 9.388359252

Solving
-9.25925926 + t = 9.388359252

Solving for variable 't'.

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

Add '9.25925926' to each side of the equation.
-9.25925926 + 9.25925926 + t = 9.388359252 + 9.25925926

Combine like terms: -9.25925926 + 9.25925926 = 0.00000000
0.00000000 + t = 9.388359252 + 9.25925926
t = 9.388359252 + 9.25925926

Combine like terms: 9.388359252 + 9.25925926 = 18.647618512
t = 18.647618512

Simplifying
t = 18.647618512


Subproblem 2
t + -9.25925926 = -9.388359252

Simplifying
t + -9.25925926 = -9.388359252

Reorder the terms:
-9.25925926 + t = -9.388359252

Solving
-9.25925926 + t = -9.388359252

Solving for variable 't'.

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

Add '9.25925926' to each side of the equation.
-9.25925926 + 9.25925926 + t = -9.388359252 + 9.25925926

Combine like terms: -9.25925926 + 9.25925926 = 0.00000000
0.00000000 + t = -9.388359252 + 9.25925926
t = -9.388359252 + 9.25925926

Combine like terms: -9.388359252 + 9.25925926 = -0.129099992
t = -0.129099992

Simplifying
t = -0.129099992


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {18.647618512, -0.129099992}

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