88=-16t^2+80t

Solution for 88=-16t^2+80t equation:

Simplifying
88 = -16t2 + 80t

Reorder the terms:
88 = 80t + -16t2

Solving
88 = 80t + -16t2

Solving for variable 't'.

Reorder the terms:
88 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2

Combine like terms: 80t + -80t = 0
88 + -80t + 16t2 = 0 + -16t2 + 16t2
88 + -80t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
88 + -80t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(11 + -10t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(11 + -10t + 2t2)' equal to zero and attempt to solve:

Simplifying
11 + -10t + 2t2 = 0

Solving
11 + -10t + 2t2 = 0

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

Divide each side by '2'.
5.5 + -5t + t2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -5t + -5.5 + t2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -5t + t2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -5t + t2 = 0 + -5.5
-5t + t2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-5t + t2 = -5.5

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -5.5 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -5.5 + 6.25

Combine like terms: -5.5 + 6.25 = 0.75
6.25 + -5t + t2 = 0.75

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(t + -2.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
t + -2.5 = 0.866025404

Simplifying
t + -2.5 = 0.866025404

Reorder the terms:
-2.5 + t = 0.866025404

Solving
-2.5 + t = 0.866025404

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 0.866025404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 0.866025404 + 2.5
t = 0.866025404 + 2.5

Combine like terms: 0.866025404 + 2.5 = 3.366025404
t = 3.366025404

Simplifying
t = 3.366025404

Subproblem 2
t + -2.5 = -0.866025404

Simplifying
t + -2.5 = -0.866025404

Reorder the terms:
-2.5 + t = -0.866025404

Solving
-2.5 + t = -0.866025404

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -0.866025404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -0.866025404 + 2.5
t = -0.866025404 + 2.5

Combine like terms: -0.866025404 + 2.5 = 1.633974596
t = 1.633974596

Simplifying
t = 1.633974596

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.366025404, 1.633974596}
Solution
t = {3.366025404, 1.633974596}