128=-16t^2+112t+0

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Solution for 128=-16t^2+112t+0 equation: 


Simplifying
128 = -16t2 + 112t + 0

Reorder the terms:
128 = 0 + 112t + -16t2
Remove the zero:
128 = 112t + -16t2

Solving
128 = 112t + -16t2

Solving for variable 't'.

Reorder the terms:
128 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2

Combine like terms: 112t + -112t = 0
128 + -112t + 16t2 = 0 + -16t2 + 16t2
128 + -112t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
128 + -112t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(8 + -7t + t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(8 + -7t + t2)' equal to zero and attempt to solve:

Simplifying
8 + -7t + t2 = 0

Solving
8 + -7t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7t + -8 + t2 = 0 + -8

Reorder the terms:
8 + -8 + -7t + t2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7t + t2 = 0 + -8
-7t + t2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7t + t2 = -8

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = -8 + 12.25

Reorder the terms:
12.25 + -7t + t2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7t + t2 = 4.25

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(t + -3.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
t + -3.5 = 2.061552813

Simplifying
t + -3.5 = 2.061552813

Reorder the terms:
-3.5 + t = 2.061552813

Solving
-3.5 + t = 2.061552813

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 2.061552813 + 3.5
t = 2.061552813 + 3.5

Combine like terms: 2.061552813 + 3.5 = 5.561552813
t = 5.561552813

Simplifying
t = 5.561552813


Subproblem 2
t + -3.5 = -2.061552813

Simplifying
t + -3.5 = -2.061552813

Reorder the terms:
-3.5 + t = -2.061552813

Solving
-3.5 + t = -2.061552813

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -2.061552813 + 3.5
t = -2.061552813 + 3.5

Combine like terms: -2.061552813 + 3.5 = 1.438447187
t = 1.438447187

Simplifying
t = 1.438447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.561552813, 1.438447187}
Solution
t = {5.561552813, 1.438447187}

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