-16t^2+88t+18=100

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Solution for -16t^2+88t+18=100 equation: 


Simplifying
-16t2 + 88t + 18 = 100

Reorder the terms:
18 + 88t + -16t2 = 100

Solving
18 + 88t + -16t2 = 100

Solving for variable 't'.

Reorder the terms:
18 + -100 + 88t + -16t2 = 100 + -100

Combine like terms: 18 + -100 = -82
-82 + 88t + -16t2 = 100 + -100

Combine like terms: 100 + -100 = 0
-82 + 88t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + 44t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-41 + 44t + -8t2)' equal to zero and attempt to solve:

Simplifying
-41 + 44t + -8t2 = 0

Solving
-41 + 44t + -8t2 = 0

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

Divide each side by '-8'.
5.125 + -5.5t + t2 = 0

Move the constant term to the right:

Add '-5.125' to each side of the equation.
5.125 + -5.5t + -5.125 + t2 = 0 + -5.125

Reorder the terms:
5.125 + -5.125 + -5.5t + t2 = 0 + -5.125

Combine like terms: 5.125 + -5.125 = 0.000
0.000 + -5.5t + t2 = 0 + -5.125
-5.5t + t2 = 0 + -5.125

Combine like terms: 0 + -5.125 = -5.125
-5.5t + t2 = -5.125

The t term is -5.5t.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5t + 7.5625 + t2 = -5.125 + 7.5625

Reorder the terms:
7.5625 + -5.5t + t2 = -5.125 + 7.5625

Combine like terms: -5.125 + 7.5625 = 2.4375
7.5625 + -5.5t + t2 = 2.4375

Factor a perfect square on the left side:
(t + -2.75)(t + -2.75) = 2.4375

Calculate the square root of the right side: 1.5612495

Break this problem into two subproblems by setting 
(t + -2.75) equal to 1.5612495 and -1.5612495.


Subproblem 1
t + -2.75 = 1.5612495

Simplifying
t + -2.75 = 1.5612495

Reorder the terms:
-2.75 + t = 1.5612495

Solving
-2.75 + t = 1.5612495

Solving for variable 't'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + t = 1.5612495 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + t = 1.5612495 + 2.75
t = 1.5612495 + 2.75

Combine like terms: 1.5612495 + 2.75 = 4.3112495
t = 4.3112495

Simplifying
t = 4.3112495


Subproblem 2
t + -2.75 = -1.5612495

Simplifying
t + -2.75 = -1.5612495

Reorder the terms:
-2.75 + t = -1.5612495

Solving
-2.75 + t = -1.5612495

Solving for variable 't'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + t = -1.5612495 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + t = -1.5612495 + 2.75
t = -1.5612495 + 2.75

Combine like terms: -1.5612495 + 2.75 = 1.1887505
t = 1.1887505

Simplifying
t = 1.1887505


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.3112495, 1.1887505}
Solution
t = {4.3112495, 1.1887505}

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