-16t^2+250t-50=0

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Solution for -16t^2+250t-50=0 equation: 


Simplifying
-16t2 + 250t + -50 = 0

Reorder the terms:
-50 + 250t + -16t2 = 0

Solving
-50 + 250t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 125t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 125t + -8t2)' equal to zero and attempt to solve:

Simplifying
-25 + 125t + -8t2 = 0

Solving
-25 + 125t + -8t2 = 0

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

Divide each side by '-8'.
3.125 + -15.625t + t2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + -15.625t + -3.125 + t2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + -15.625t + t2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + -15.625t + t2 = 0 + -3.125
-15.625t + t2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
-15.625t + t2 = -3.125

The t term is -15.625t.  Take half its coefficient (-7.8125).
Square it (61.03515625) and add it to both sides.

Add '61.03515625' to each side of the equation.
-15.625t + 61.03515625 + t2 = -3.125 + 61.03515625

Reorder the terms:
61.03515625 + -15.625t + t2 = -3.125 + 61.03515625

Combine like terms: -3.125 + 61.03515625 = 57.91015625
61.03515625 + -15.625t + t2 = 57.91015625

Factor a perfect square on the left side:
(t + -7.8125)(t + -7.8125) = 57.91015625

Calculate the square root of the right side: 7.609872289

Break this problem into two subproblems by setting 
(t + -7.8125) equal to 7.609872289 and -7.609872289.


Subproblem 1
t + -7.8125 = 7.609872289

Simplifying
t + -7.8125 = 7.609872289

Reorder the terms:
-7.8125 + t = 7.609872289

Solving
-7.8125 + t = 7.609872289

Solving for variable 't'.

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

Add '7.8125' to each side of the equation.
-7.8125 + 7.8125 + t = 7.609872289 + 7.8125

Combine like terms: -7.8125 + 7.8125 = 0.0000
0.0000 + t = 7.609872289 + 7.8125
t = 7.609872289 + 7.8125

Combine like terms: 7.609872289 + 7.8125 = 15.422372289
t = 15.422372289

Simplifying
t = 15.422372289


Subproblem 2
t + -7.8125 = -7.609872289

Simplifying
t + -7.8125 = -7.609872289

Reorder the terms:
-7.8125 + t = -7.609872289

Solving
-7.8125 + t = -7.609872289

Solving for variable 't'.

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

Add '7.8125' to each side of the equation.
-7.8125 + 7.8125 + t = -7.609872289 + 7.8125

Combine like terms: -7.8125 + 7.8125 = 0.0000
0.0000 + t = -7.609872289 + 7.8125
t = -7.609872289 + 7.8125

Combine like terms: -7.609872289 + 7.8125 = 0.202627711
t = 0.202627711

Simplifying
t = 0.202627711


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {15.422372289, 0.202627711}
Solution
t = {15.422372289, 0.202627711}

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