-16t^2+10t+50=0

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Solution for -16t^2+10t+50=0 equation: 


Simplifying
-16t2 + 10t + 50 = 0

Reorder the terms:
50 + 10t + -16t2 = 0

Solving
50 + 10t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 5t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 5t + -8t2)' equal to zero and attempt to solve:

Simplifying
25 + 5t + -8t2 = 0

Solving
25 + 5t + -8t2 = 0

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

Divide each side by '-8'.
-3.125 + -0.625t + t2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -0.625t + 3.125 + t2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -0.625t + t2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -0.625t + t2 = 0 + 3.125
-0.625t + t2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-0.625t + t2 = 3.125

The t term is -0.625t.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625t + 0.09765625 + t2 = 3.125 + 0.09765625

Reorder the terms:
0.09765625 + -0.625t + t2 = 3.125 + 0.09765625

Combine like terms: 3.125 + 0.09765625 = 3.22265625
0.09765625 + -0.625t + t2 = 3.22265625

Factor a perfect square on the left side:
(t + -0.3125)(t + -0.3125) = 3.22265625

Calculate the square root of the right side: 1.795175827

Break this problem into two subproblems by setting 
(t + -0.3125) equal to 1.795175827 and -1.795175827.


Subproblem 1
t + -0.3125 = 1.795175827

Simplifying
t + -0.3125 = 1.795175827

Reorder the terms:
-0.3125 + t = 1.795175827

Solving
-0.3125 + t = 1.795175827

Solving for variable 't'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + t = 1.795175827 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + t = 1.795175827 + 0.3125
t = 1.795175827 + 0.3125

Combine like terms: 1.795175827 + 0.3125 = 2.107675827
t = 2.107675827

Simplifying
t = 2.107675827


Subproblem 2
t + -0.3125 = -1.795175827

Simplifying
t + -0.3125 = -1.795175827

Reorder the terms:
-0.3125 + t = -1.795175827

Solving
-0.3125 + t = -1.795175827

Solving for variable 't'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + t = -1.795175827 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + t = -1.795175827 + 0.3125
t = -1.795175827 + 0.3125

Combine like terms: -1.795175827 + 0.3125 = -1.482675827
t = -1.482675827

Simplifying
t = -1.482675827


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.107675827, -1.482675827}
Solution
t = {2.107675827, -1.482675827}

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