-16t^2+90t+110=0

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Solution for -16t^2+90t+110=0 equation: 


Simplifying
-16t2 + 90t + 110 = 0

Reorder the terms:
110 + 90t + -16t2 = 0

Solving
110 + 90t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + 45t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(55 + 45t + -8t2)' equal to zero and attempt to solve:

Simplifying
55 + 45t + -8t2 = 0

Solving
55 + 45t + -8t2 = 0

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

Divide each side by '-8'.
-6.875 + -5.625t + t2 = 0

Move the constant term to the right:

Add '6.875' to each side of the equation.
-6.875 + -5.625t + 6.875 + t2 = 0 + 6.875

Reorder the terms:
-6.875 + 6.875 + -5.625t + t2 = 0 + 6.875

Combine like terms: -6.875 + 6.875 = 0.000
0.000 + -5.625t + t2 = 0 + 6.875
-5.625t + t2 = 0 + 6.875

Combine like terms: 0 + 6.875 = 6.875
-5.625t + t2 = 6.875

The t term is -5.625t.  Take half its coefficient (-2.8125).
Square it (7.91015625) and add it to both sides.

Add '7.91015625' to each side of the equation.
-5.625t + 7.91015625 + t2 = 6.875 + 7.91015625

Reorder the terms:
7.91015625 + -5.625t + t2 = 6.875 + 7.91015625

Combine like terms: 6.875 + 7.91015625 = 14.78515625
7.91015625 + -5.625t + t2 = 14.78515625

Factor a perfect square on the left side:
(t + -2.8125)(t + -2.8125) = 14.78515625

Calculate the square root of the right side: 3.845147104

Break this problem into two subproblems by setting 
(t + -2.8125) equal to 3.845147104 and -3.845147104.


Subproblem 1
t + -2.8125 = 3.845147104

Simplifying
t + -2.8125 = 3.845147104

Reorder the terms:
-2.8125 + t = 3.845147104

Solving
-2.8125 + t = 3.845147104

Solving for variable 't'.

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

Add '2.8125' to each side of the equation.
-2.8125 + 2.8125 + t = 3.845147104 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + t = 3.845147104 + 2.8125
t = 3.845147104 + 2.8125

Combine like terms: 3.845147104 + 2.8125 = 6.657647104
t = 6.657647104

Simplifying
t = 6.657647104


Subproblem 2
t + -2.8125 = -3.845147104

Simplifying
t + -2.8125 = -3.845147104

Reorder the terms:
-2.8125 + t = -3.845147104

Solving
-2.8125 + t = -3.845147104

Solving for variable 't'.

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

Add '2.8125' to each side of the equation.
-2.8125 + 2.8125 + t = -3.845147104 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + t = -3.845147104 + 2.8125
t = -3.845147104 + 2.8125

Combine like terms: -3.845147104 + 2.8125 = -1.032647104
t = -1.032647104

Simplifying
t = -1.032647104


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.657647104, -1.032647104}
Solution
t = {6.657647104, -1.032647104}

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