16t^2+100t=50

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Solution for 16t^2+100t=50 equation: 


Simplifying
16t2 + 100t = 50

Reorder the terms:
100t + 16t2 = 50

Solving
100t + 16t2 = 50

Solving for variable 't'.

Reorder the terms:
-50 + 100t + 16t2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 100t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 50t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 50t + 8t2)' equal to zero and attempt to solve:

Simplifying
-25 + 50t + 8t2 = 0

Solving
-25 + 50t + 8t2 = 0

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

Divide each side by '8'.
-3.125 + 6.25t + t2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + 6.25t + 3.125 + t2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + 6.25t + t2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + 6.25t + t2 = 0 + 3.125
6.25t + t2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
6.25t + t2 = 3.125

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 = 3.125 + 9.765625

Reorder the terms:
9.765625 + 6.25t + t2 = 3.125 + 9.765625

Combine like terms: 3.125 + 9.765625 = 12.890625
9.765625 + 6.25t + t2 = 12.890625

Factor a perfect square on the left side:
(t + 3.125)(t + 3.125) = 12.890625

Calculate the square root of the right side: 3.590351654

Break this problem into two subproblems by setting 
(t + 3.125) equal to 3.590351654 and -3.590351654.


Subproblem 1
t + 3.125 = 3.590351654

Simplifying
t + 3.125 = 3.590351654

Reorder the terms:
3.125 + t = 3.590351654

Solving
3.125 + t = 3.590351654

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 = 3.590351654 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + t = 3.590351654 + -3.125
t = 3.590351654 + -3.125

Combine like terms: 3.590351654 + -3.125 = 0.465351654
t = 0.465351654

Simplifying
t = 0.465351654


Subproblem 2
t + 3.125 = -3.590351654

Simplifying
t + 3.125 = -3.590351654

Reorder the terms:
3.125 + t = -3.590351654

Solving
3.125 + t = -3.590351654

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 = -3.590351654 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + t = -3.590351654 + -3.125
t = -3.590351654 + -3.125

Combine like terms: -3.590351654 + -3.125 = -6.715351654
t = -6.715351654

Simplifying
t = -6.715351654


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.465351654, -6.715351654}
Solution
t = {0.465351654, -6.715351654}

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