1000(30+17t-t^2)=0

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Solution for 1000(30+17t-t^2)=0 equation: 


Simplifying
1000(30 + 17t + -1t2) = 0
(30 * 1000 + 17t * 1000 + -1t2 * 1000) = 0
(30000 + 17000t + -1000t2) = 0

Solving
30000 + 17000t + -1000t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '1000'.
1000(30 + 17t + -1t2) = 0

Ignore the factor 1000.

Subproblem 1
Set the factor '(30 + 17t + -1t2)' equal to zero and attempt to solve:

Simplifying
30 + 17t + -1t2 = 0

Solving
30 + 17t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + -17t + t2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -17t + 30 + t2 = 0 + 30

Reorder the terms:
-30 + 30 + -17t + t2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -17t + t2 = 0 + 30
-17t + t2 = 0 + 30

Combine like terms: 0 + 30 = 30
-17t + t2 = 30

The t term is -17t.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17t + 72.25 + t2 = 30 + 72.25

Reorder the terms:
72.25 + -17t + t2 = 30 + 72.25

Combine like terms: 30 + 72.25 = 102.25
72.25 + -17t + t2 = 102.25

Factor a perfect square on the left side:
(t + -8.5)(t + -8.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(t + -8.5) equal to 10.111874208 and -10.111874208.


Subproblem 1
t + -8.5 = 10.111874208

Simplifying
t + -8.5 = 10.111874208

Reorder the terms:
-8.5 + t = 10.111874208

Solving
-8.5 + t = 10.111874208

Solving for variable 't'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + t = 10.111874208 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + t = 10.111874208 + 8.5
t = 10.111874208 + 8.5

Combine like terms: 10.111874208 + 8.5 = 18.611874208
t = 18.611874208

Simplifying
t = 18.611874208


Subproblem 2
t + -8.5 = -10.111874208

Simplifying
t + -8.5 = -10.111874208

Reorder the terms:
-8.5 + t = -10.111874208

Solving
-8.5 + t = -10.111874208

Solving for variable 't'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + t = -10.111874208 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + t = -10.111874208 + 8.5
t = -10.111874208 + 8.5

Combine like terms: -10.111874208 + 8.5 = -1.611874208
t = -1.611874208

Simplifying
t = -1.611874208


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {18.611874208, -1.611874208}
Solution
t = {18.611874208, -1.611874208}

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