-16t^2+200t+50=0

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Solution for -16t^2+200t+50=0 equation: 


Simplifying
-16t2 + 200t + 50 = 0

Reorder the terms:
50 + 200t + -16t2 = 0

Solving
50 + 200t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 100t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 100t + -8t2)' equal to zero and attempt to solve:

Simplifying
25 + 100t + -8t2 = 0

Solving
25 + 100t + -8t2 = 0

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

Divide each side by '-8'.
-3.125 + -12.5t + t2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -12.5t + 3.125 + t2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -12.5t + t2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -12.5t + t2 = 0 + 3.125
-12.5t + t2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-12.5t + t2 = 3.125

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 = 3.125 + 39.0625

Reorder the terms:
39.0625 + -12.5t + t2 = 3.125 + 39.0625

Combine like terms: 3.125 + 39.0625 = 42.1875
39.0625 + -12.5t + t2 = 42.1875

Factor a perfect square on the left side:
(t + -6.25)(t + -6.25) = 42.1875

Calculate the square root of the right side: 6.495190528

Break this problem into two subproblems by setting 
(t + -6.25) equal to 6.495190528 and -6.495190528.


Subproblem 1
t + -6.25 = 6.495190528

Simplifying
t + -6.25 = 6.495190528

Reorder the terms:
-6.25 + t = 6.495190528

Solving
-6.25 + t = 6.495190528

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 = 6.495190528 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + t = 6.495190528 + 6.25
t = 6.495190528 + 6.25

Combine like terms: 6.495190528 + 6.25 = 12.745190528
t = 12.745190528

Simplifying
t = 12.745190528


Subproblem 2
t + -6.25 = -6.495190528

Simplifying
t + -6.25 = -6.495190528

Reorder the terms:
-6.25 + t = -6.495190528

Solving
-6.25 + t = -6.495190528

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 = -6.495190528 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + t = -6.495190528 + 6.25
t = -6.495190528 + 6.25

Combine like terms: -6.495190528 + 6.25 = -0.245190528
t = -0.245190528

Simplifying
t = -0.245190528


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.745190528, -0.245190528}
Solution
t = {12.745190528, -0.245190528}

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