t^2(2-18)+96t+1000=0

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Solution for t^2(2-18)+96t+1000=0 equation: 


Simplifying
t2(2 + -18) + 96t + 1000 = 0

Combine like terms: 2 + -18 = -16
t2(-16) + 96t + 1000 = 0

Reorder the terms for easier multiplication:
-16t2 + 96t + 1000 = 0

Reorder the terms:
1000 + 96t + -16t2 = 0

Solving
1000 + 96t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(125 + 12t + -2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(125 + 12t + -2t2)' equal to zero and attempt to solve:

Simplifying
125 + 12t + -2t2 = 0

Solving
125 + 12t + -2t2 = 0

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

Divide each side by '-2'.
-62.5 + -6t + t2 = 0

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + -6t + 62.5 + t2 = 0 + 62.5

Reorder the terms:
-62.5 + 62.5 + -6t + t2 = 0 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + -6t + t2 = 0 + 62.5
-6t + t2 = 0 + 62.5

Combine like terms: 0 + 62.5 = 62.5
-6t + t2 = 62.5

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 62.5 + 9

Reorder the terms:
9 + -6t + t2 = 62.5 + 9

Combine like terms: 62.5 + 9 = 71.5
9 + -6t + t2 = 71.5

Factor a perfect square on the left side:
(t + -3)(t + -3) = 71.5

Calculate the square root of the right side: 8.455767263

Break this problem into two subproblems by setting 
(t + -3) equal to 8.455767263 and -8.455767263.


Subproblem 1
t + -3 = 8.455767263

Simplifying
t + -3 = 8.455767263

Reorder the terms:
-3 + t = 8.455767263

Solving
-3 + t = 8.455767263

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 8.455767263 + 3

Combine like terms: -3 + 3 = 0
0 + t = 8.455767263 + 3
t = 8.455767263 + 3

Combine like terms: 8.455767263 + 3 = 11.455767263
t = 11.455767263

Simplifying
t = 11.455767263


Subproblem 2
t + -3 = -8.455767263

Simplifying
t + -3 = -8.455767263

Reorder the terms:
-3 + t = -8.455767263

Solving
-3 + t = -8.455767263

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -8.455767263 + 3

Combine like terms: -3 + 3 = 0
0 + t = -8.455767263 + 3
t = -8.455767263 + 3

Combine like terms: -8.455767263 + 3 = -5.455767263
t = -5.455767263

Simplifying
t = -5.455767263


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.455767263, -5.455767263}
Solution
t = {11.455767263, -5.455767263}

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