2.85t^2+50t-1000=0

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Solution for 2.85t^2+50t-1000=0 equation: 


Simplifying
2.85t2 + 50t + -1000 = 0

Reorder the terms:
-1000 + 50t + 2.85t2 = 0

Solving
-1000 + 50t + 2.85t2 = 0

Solving for variable 't'.

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

Divide each side by '2.85'.
-350.877193 + 17.54385965t + t2 = 0

Move the constant term to the right:

Add '350.877193' to each side of the equation.
-350.877193 + 17.54385965t + 350.877193 + t2 = 0 + 350.877193

Reorder the terms:
-350.877193 + 350.877193 + 17.54385965t + t2 = 0 + 350.877193

Combine like terms: -350.877193 + 350.877193 = 0.000000
0.000000 + 17.54385965t + t2 = 0 + 350.877193
17.54385965t + t2 = 0 + 350.877193

Combine like terms: 0 + 350.877193 = 350.877193
17.54385965t + t2 = 350.877193

The t term is 17.54385965t.  Take half its coefficient (8.771929825).
Square it (76.94675285) and add it to both sides.

Add '76.94675285' to each side of the equation.
17.54385965t + 76.94675285 + t2 = 350.877193 + 76.94675285

Reorder the terms:
76.94675285 + 17.54385965t + t2 = 350.877193 + 76.94675285

Combine like terms: 350.877193 + 76.94675285 = 427.82394585
76.94675285 + 17.54385965t + t2 = 427.82394585

Factor a perfect square on the left side:
(t + 8.771929825)(t + 8.771929825) = 427.82394585

Calculate the square root of the right side: 20.683905479

Break this problem into two subproblems by setting 
(t + 8.771929825) equal to 20.683905479 and -20.683905479.


Subproblem 1
t + 8.771929825 = 20.683905479

Simplifying
t + 8.771929825 = 20.683905479

Reorder the terms:
8.771929825 + t = 20.683905479

Solving
8.771929825 + t = 20.683905479

Solving for variable 't'.

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

Add '-8.771929825' to each side of the equation.
8.771929825 + -8.771929825 + t = 20.683905479 + -8.771929825

Combine like terms: 8.771929825 + -8.771929825 = 0.000000000
0.000000000 + t = 20.683905479 + -8.771929825
t = 20.683905479 + -8.771929825

Combine like terms: 20.683905479 + -8.771929825 = 11.911975654
t = 11.911975654

Simplifying
t = 11.911975654


Subproblem 2
t + 8.771929825 = -20.683905479

Simplifying
t + 8.771929825 = -20.683905479

Reorder the terms:
8.771929825 + t = -20.683905479

Solving
8.771929825 + t = -20.683905479

Solving for variable 't'.

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

Add '-8.771929825' to each side of the equation.
8.771929825 + -8.771929825 + t = -20.683905479 + -8.771929825

Combine like terms: 8.771929825 + -8.771929825 = 0.000000000
0.000000000 + t = -20.683905479 + -8.771929825
t = -20.683905479 + -8.771929825

Combine like terms: -20.683905479 + -8.771929825 = -29.455835304
t = -29.455835304

Simplifying
t = -29.455835304


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.911975654, -29.455835304}

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