-.3t^2+5t+5=0

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Solution for -.3t^2+5t+5=0 equation:


Simplifying
-0.3t2 + 5t + 5 = 0

Reorder the terms:
5 + 5t + -0.3t2 = 0

Solving
5 + 5t + -0.3t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
-16.66666667 + -16.66666667t + t2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -16.66666667t + 16.66666667 + t2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -16.66666667t + t2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -16.66666667t + t2 = 0 + 16.66666667
-16.66666667t + t2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-16.66666667t + t2 = 16.66666667

The t term is -16.66666667t.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667t + 69.44444447 + t2 = 16.66666667 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667t + t2 = 16.66666667 + 69.44444447

Combine like terms: 16.66666667 + 69.44444447 = 86.11111114
69.44444447 + -16.66666667t + t2 = 86.11111114

Factor a perfect square on the left side:
(t + -8.333333335)(t + -8.333333335) = 86.11111114

Calculate the square root of the right side: 9.279607273

Break this problem into two subproblems by setting 
(t + -8.333333335) equal to 9.279607273 and -9.279607273.


Subproblem 1
t + -8.333333335 = 9.279607273

Simplifying
t + -8.333333335 = 9.279607273

Reorder the terms:
-8.333333335 + t = 9.279607273

Solving
-8.333333335 + t = 9.279607273

Solving for variable 't'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + t = 9.279607273 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = 9.279607273 + 8.333333335
t = 9.279607273 + 8.333333335

Combine like terms: 9.279607273 + 8.333333335 = 17.612940608
t = 17.612940608

Simplifying
t = 17.612940608


Subproblem 2
t + -8.333333335 = -9.279607273

Simplifying
t + -8.333333335 = -9.279607273

Reorder the terms:
-8.333333335 + t = -9.279607273

Solving
-8.333333335 + t = -9.279607273

Solving for variable 't'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + t = -9.279607273 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = -9.279607273 + 8.333333335
t = -9.279607273 + 8.333333335

Combine like terms: -9.279607273 + 8.333333335 = -0.946273938
t = -0.946273938

Simplifying
t = -0.946273938


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {17.612940608, -0.946273938}

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