-16t^2+64t+200=0

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Solution for -16t^2+64t+200=0 equation: 


Simplifying
-16t2 + 64t + 200 = 0

Reorder the terms:
200 + 64t + -16t2 = 0

Solving
200 + 64t + -16t2 = 0

Solving for variable 't'.

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

Ignore the factor 8.

Subproblem 1
Set the factor '(25 + 8t + -2t2)' equal to zero and attempt to solve:

Simplifying
25 + 8t + -2t2 = 0

Solving
25 + 8t + -2t2 = 0

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

Divide each side by '-2'.
-12.5 + -4t + t2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -4t + 12.5 + t2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -4t + t2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -4t + t2 = 0 + 12.5
-4t + t2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-4t + t2 = 12.5

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 12.5 + 4

Reorder the terms:
4 + -4t + t2 = 12.5 + 4

Combine like terms: 12.5 + 4 = 16.5
4 + -4t + t2 = 16.5

Factor a perfect square on the left side:
(t + -2)(t + -2) = 16.5

Calculate the square root of the right side: 4.062019202

Break this problem into two subproblems by setting 
(t + -2) equal to 4.062019202 and -4.062019202.


Subproblem 1
t + -2 = 4.062019202

Simplifying
t + -2 = 4.062019202

Reorder the terms:
-2 + t = 4.062019202

Solving
-2 + t = 4.062019202

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 4.062019202 + 2

Combine like terms: -2 + 2 = 0
0 + t = 4.062019202 + 2
t = 4.062019202 + 2

Combine like terms: 4.062019202 + 2 = 6.062019202
t = 6.062019202

Simplifying
t = 6.062019202


Subproblem 2
t + -2 = -4.062019202

Simplifying
t + -2 = -4.062019202

Reorder the terms:
-2 + t = -4.062019202

Solving
-2 + t = -4.062019202

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -4.062019202 + 2

Combine like terms: -2 + 2 = 0
0 + t = -4.062019202 + 2
t = -4.062019202 + 2

Combine like terms: -4.062019202 + 2 = -2.062019202
t = -2.062019202

Simplifying
t = -2.062019202


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.062019202, -2.062019202}
Solution
t = {6.062019202, -2.062019202}

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