-16t^2+100t+250=-200

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Solution for -16t^2+100t+250=-200 equation: 


Simplifying
-16t2 + 100t + 250 = -200

Reorder the terms:
250 + 100t + -16t2 = -200

Solving
250 + 100t + -16t2 = -200

Solving for variable 't'.

Reorder the terms:
250 + 200 + 100t + -16t2 = -200 + 200

Combine like terms: 250 + 200 = 450
450 + 100t + -16t2 = -200 + 200

Combine like terms: -200 + 200 = 0
450 + 100t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(225 + 50t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(225 + 50t + -8t2)' equal to zero and attempt to solve:

Simplifying
225 + 50t + -8t2 = 0

Solving
225 + 50t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-28.125 + -6.25t + t2 = 0

Move the constant term to the right:

Add '28.125' to each side of the equation.
-28.125 + -6.25t + 28.125 + t2 = 0 + 28.125

Reorder the terms:
-28.125 + 28.125 + -6.25t + t2 = 0 + 28.125

Combine like terms: -28.125 + 28.125 = 0.000
0.000 + -6.25t + t2 = 0 + 28.125
-6.25t + t2 = 0 + 28.125

Combine like terms: 0 + 28.125 = 28.125
-6.25t + t2 = 28.125

The t term is -6.25t.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25t + 9.765625 + t2 = 28.125 + 9.765625

Reorder the terms:
9.765625 + -6.25t + t2 = 28.125 + 9.765625

Combine like terms: 28.125 + 9.765625 = 37.890625
9.765625 + -6.25t + t2 = 37.890625

Factor a perfect square on the left side:
(t + -3.125)(t + -3.125) = 37.890625

Calculate the square root of the right side: 6.155536126

Break this problem into two subproblems by setting 
(t + -3.125) equal to 6.155536126 and -6.155536126.


Subproblem 1
t + -3.125 = 6.155536126

Simplifying
t + -3.125 = 6.155536126

Reorder the terms:
-3.125 + t = 6.155536126

Solving
-3.125 + t = 6.155536126

Solving for variable 't'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + t = 6.155536126 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = 6.155536126 + 3.125
t = 6.155536126 + 3.125

Combine like terms: 6.155536126 + 3.125 = 9.280536126
t = 9.280536126

Simplifying
t = 9.280536126


Subproblem 2
t + -3.125 = -6.155536126

Simplifying
t + -3.125 = -6.155536126

Reorder the terms:
-3.125 + t = -6.155536126

Solving
-3.125 + t = -6.155536126

Solving for variable 't'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + t = -6.155536126 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = -6.155536126 + 3.125
t = -6.155536126 + 3.125

Combine like terms: -6.155536126 + 3.125 = -3.030536126
t = -3.030536126

Simplifying
t = -3.030536126


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.280536126, -3.030536126}
Solution
t = {9.280536126, -3.030536126}

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