-16t^2+120t+500=200

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Solution for -16t^2+120t+500=200 equation: 


Simplifying
-16t2 + 120t + 500 = 200

Reorder the terms:
500 + 120t + -16t2 = 200

Solving
500 + 120t + -16t2 = 200

Solving for variable 't'.

Reorder the terms:
500 + -200 + 120t + -16t2 = 200 + -200

Combine like terms: 500 + -200 = 300
300 + 120t + -16t2 = 200 + -200

Combine like terms: 200 + -200 = 0
300 + 120t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(75 + 30t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(75 + 30t + -4t2)' equal to zero and attempt to solve:

Simplifying
75 + 30t + -4t2 = 0

Solving
75 + 30t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-18.75 + -7.5t + t2 = 0

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + -7.5t + 18.75 + t2 = 0 + 18.75

Reorder the terms:
-18.75 + 18.75 + -7.5t + t2 = 0 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + -7.5t + t2 = 0 + 18.75
-7.5t + t2 = 0 + 18.75

Combine like terms: 0 + 18.75 = 18.75
-7.5t + t2 = 18.75

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = 18.75 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = 18.75 + 14.0625

Combine like terms: 18.75 + 14.0625 = 32.8125
14.0625 + -7.5t + t2 = 32.8125

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 32.8125

Calculate the square root of the right side: 5.728219619

Break this problem into two subproblems by setting 
(t + -3.75) equal to 5.728219619 and -5.728219619.


Subproblem 1
t + -3.75 = 5.728219619

Simplifying
t + -3.75 = 5.728219619

Reorder the terms:
-3.75 + t = 5.728219619

Solving
-3.75 + t = 5.728219619

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 5.728219619 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 5.728219619 + 3.75
t = 5.728219619 + 3.75

Combine like terms: 5.728219619 + 3.75 = 9.478219619
t = 9.478219619

Simplifying
t = 9.478219619


Subproblem 2
t + -3.75 = -5.728219619

Simplifying
t + -3.75 = -5.728219619

Reorder the terms:
-3.75 + t = -5.728219619

Solving
-3.75 + t = -5.728219619

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -5.728219619 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -5.728219619 + 3.75
t = -5.728219619 + 3.75

Combine like terms: -5.728219619 + 3.75 = -1.978219619
t = -1.978219619

Simplifying
t = -1.978219619


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.478219619, -1.978219619}
Solution
t = {9.478219619, -1.978219619}

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