200t=-16t^2+200

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Solution for 200t=-16t^2+200 equation: 


Simplifying
200t = -16t2 + 200

Reorder the terms:
200t = 200 + -16t2

Solving
200t = 200 + -16t2

Solving for variable 't'.

Reorder the terms:
-200 + 200t + 16t2 = 200 + -16t2 + -200 + 16t2

Reorder the terms:
-200 + 200t + 16t2 = 200 + -200 + -16t2 + 16t2

Combine like terms: 200 + -200 = 0
-200 + 200t + 16t2 = 0 + -16t2 + 16t2
-200 + 200t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-200 + 200t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-25 + 25t + 2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-25 + 25t + 2t2)' equal to zero and attempt to solve:

Simplifying
-25 + 25t + 2t2 = 0

Solving
-25 + 25t + 2t2 = 0

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

Divide each side by '2'.
-12.5 + 12.5t + t2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 12.5t + 12.5 + t2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 12.5t + t2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 12.5t + t2 = 0 + 12.5
12.5t + t2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
12.5t + t2 = 12.5

The t term is 12.5t.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5t + 39.0625 + t2 = 12.5 + 39.0625

Reorder the terms:
39.0625 + 12.5t + t2 = 12.5 + 39.0625

Combine like terms: 12.5 + 39.0625 = 51.5625
39.0625 + 12.5t + t2 = 51.5625

Factor a perfect square on the left side:
(t + 6.25)(t + 6.25) = 51.5625

Calculate the square root of the right side: 7.180703308

Break this problem into two subproblems by setting 
(t + 6.25) equal to 7.180703308 and -7.180703308.


Subproblem 1
t + 6.25 = 7.180703308

Simplifying
t + 6.25 = 7.180703308

Reorder the terms:
6.25 + t = 7.180703308

Solving
6.25 + t = 7.180703308

Solving for variable 't'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + t = 7.180703308 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + t = 7.180703308 + -6.25
t = 7.180703308 + -6.25

Combine like terms: 7.180703308 + -6.25 = 0.930703308
t = 0.930703308

Simplifying
t = 0.930703308


Subproblem 2
t + 6.25 = -7.180703308

Simplifying
t + 6.25 = -7.180703308

Reorder the terms:
6.25 + t = -7.180703308

Solving
6.25 + t = -7.180703308

Solving for variable 't'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + t = -7.180703308 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + t = -7.180703308 + -6.25
t = -7.180703308 + -6.25

Combine like terms: -7.180703308 + -6.25 = -13.430703308
t = -13.430703308

Simplifying
t = -13.430703308


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.930703308, -13.430703308}
Solution
t = {0.930703308, -13.430703308}

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