-16t^2-10t+110=0

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Solution for -16t^2-10t+110=0 equation: 


Simplifying
-16t2 + -10t + 110 = 0

Reorder the terms:
110 + -10t + -16t2 = 0

Solving
110 + -10t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + -5t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(55 + -5t + -8t2)' equal to zero and attempt to solve:

Simplifying
55 + -5t + -8t2 = 0

Solving
55 + -5t + -8t2 = 0

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

Divide each side by '-8'.
-6.875 + 0.625t + t2 = 0

Move the constant term to the right:

Add '6.875' to each side of the equation.
-6.875 + 0.625t + 6.875 + t2 = 0 + 6.875

Reorder the terms:
-6.875 + 6.875 + 0.625t + t2 = 0 + 6.875

Combine like terms: -6.875 + 6.875 = 0.000
0.000 + 0.625t + t2 = 0 + 6.875
0.625t + t2 = 0 + 6.875

Combine like terms: 0 + 6.875 = 6.875
0.625t + t2 = 6.875

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 = 6.875 + 0.09765625

Reorder the terms:
0.09765625 + 0.625t + t2 = 6.875 + 0.09765625

Combine like terms: 6.875 + 0.09765625 = 6.97265625
0.09765625 + 0.625t + t2 = 6.97265625

Factor a perfect square on the left side:
(t + 0.3125)(t + 0.3125) = 6.97265625

Calculate the square root of the right side: 2.640578772

Break this problem into two subproblems by setting 
(t + 0.3125) equal to 2.640578772 and -2.640578772.


Subproblem 1
t + 0.3125 = 2.640578772

Simplifying
t + 0.3125 = 2.640578772

Reorder the terms:
0.3125 + t = 2.640578772

Solving
0.3125 + t = 2.640578772

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 = 2.640578772 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = 2.640578772 + -0.3125
t = 2.640578772 + -0.3125

Combine like terms: 2.640578772 + -0.3125 = 2.328078772
t = 2.328078772

Simplifying
t = 2.328078772


Subproblem 2
t + 0.3125 = -2.640578772

Simplifying
t + 0.3125 = -2.640578772

Reorder the terms:
0.3125 + t = -2.640578772

Solving
0.3125 + t = -2.640578772

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 = -2.640578772 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = -2.640578772 + -0.3125
t = -2.640578772 + -0.3125

Combine like terms: -2.640578772 + -0.3125 = -2.953078772
t = -2.953078772

Simplifying
t = -2.953078772


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.328078772, -2.953078772}
Solution
t = {2.328078772, -2.953078772}

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