-1000=-1.057t^2+8.259t+74.071

Solution for -1000=-1.057t^2+8.259t+74.071 equation:

Simplifying
-1000 = -1.057t2 + 8.259t + 74.071

Reorder the terms:
-1000 = 74.071 + 8.259t + -1.057t2

Solving
-1000 = 74.071 + 8.259t + -1.057t2

Solving for variable 't'.

Combine like terms: -1000 + -74.071 = -1074.071
-1074.071 + -8.259t + 1.057t2 = 74.071 + 8.259t + -1.057t2 + -74.071 + -8.259t + 1.057t2

Reorder the terms:
-1074.071 + -8.259t + 1.057t2 = 74.071 + -74.071 + 8.259t + -8.259t + -1.057t2 + 1.057t2

Combine like terms: 74.071 + -74.071 = 0.000
-1074.071 + -8.259t + 1.057t2 = 0.000 + 8.259t + -8.259t + -1.057t2 + 1.057t2
-1074.071 + -8.259t + 1.057t2 = 8.259t + -8.259t + -1.057t2 + 1.057t2

Combine like terms: 8.259t + -8.259t = 0.000
-1074.071 + -8.259t + 1.057t2 = 0.000 + -1.057t2 + 1.057t2
-1074.071 + -8.259t + 1.057t2 = -1.057t2 + 1.057t2

Combine like terms: -1.057t2 + 1.057t2 = 0.000
-1074.071 + -8.259t + 1.057t2 = 0.000

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

Divide each side by '1.057'.
-1016.150426 + -7.813623463t + t2 = 0

Move the constant term to the right:

Add '1016.150426' to each side of the equation.
-1016.150426 + -7.813623463t + 1016.150426 + t2 = 0 + 1016.150426

Reorder the terms:
-1016.150426 + 1016.150426 + -7.813623463t + t2 = 0 + 1016.150426

Combine like terms: -1016.150426 + 1016.150426 = 0.000000
0.000000 + -7.813623463t + t2 = 0 + 1016.150426
-7.813623463t + t2 = 0 + 1016.150426

Combine like terms: 0 + 1016.150426 = 1016.150426
-7.813623463t + t2 = 1016.150426

The t term is -7.813623463t.  Take half its coefficient (-3.906811732).
Square it (15.26317791) and add it to both sides.

Add '15.26317791' to each side of the equation.
-7.813623463t + 15.26317791 + t2 = 1016.150426 + 15.26317791

Reorder the terms:
15.26317791 + -7.813623463t + t2 = 1016.150426 + 15.26317791

Combine like terms: 1016.150426 + 15.26317791 = 1031.41360391
15.26317791 + -7.813623463t + t2 = 1031.41360391

Factor a perfect square on the left side:
(t + -3.906811732)(t + -3.906811732) = 1031.41360391

Calculate the square root of the right side: 32.115628655

Break this problem into two subproblems by setting 
(t + -3.906811732) equal to 32.115628655 and -32.115628655.

Subproblem 1
t + -3.906811732 = 32.115628655

Simplifying
t + -3.906811732 = 32.115628655

Reorder the terms:
-3.906811732 + t = 32.115628655

Solving
-3.906811732 + t = 32.115628655

Solving for variable 't'.

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

Add '3.906811732' to each side of the equation.
-3.906811732 + 3.906811732 + t = 32.115628655 + 3.906811732

Combine like terms: -3.906811732 + 3.906811732 = 0.000000000
0.000000000 + t = 32.115628655 + 3.906811732
t = 32.115628655 + 3.906811732

Combine like terms: 32.115628655 + 3.906811732 = 36.022440387
t = 36.022440387

Simplifying
t = 36.022440387

Subproblem 2
t + -3.906811732 = -32.115628655

Simplifying
t + -3.906811732 = -32.115628655

Reorder the terms:
-3.906811732 + t = -32.115628655

Solving
-3.906811732 + t = -32.115628655

Solving for variable 't'.

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

Add '3.906811732' to each side of the equation.
-3.906811732 + 3.906811732 + t = -32.115628655 + 3.906811732

Combine like terms: -3.906811732 + 3.906811732 = 0.000000000
0.000000000 + t = -32.115628655 + 3.906811732
t = -32.115628655 + 3.906811732

Combine like terms: -32.115628655 + 3.906811732 = -28.208816923
t = -28.208816923

Simplifying
t = -28.208816923

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {36.022440387, -28.208816923}