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

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


Simplifying
112 = -16t2 + 112t + 128

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

Solving
112 = 128 + 112t + -16t2

Solving for variable 't'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '16'.
16(-1 + -7t + t2) = 0

Ignore the factor 16.

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

Simplifying
-1 + -7t + t2 = 0

Solving
-1 + -7t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -7t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -7t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7t + t2 = 0 + 1
-7t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-7t + t2 = 1

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 = 1 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + -7t + t2 = 13.25

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(t + -3.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
t + -3.5 = 3.640054945

Simplifying
t + -3.5 = 3.640054945

Reorder the terms:
-3.5 + t = 3.640054945

Solving
-3.5 + t = 3.640054945

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 = 3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 3.640054945 + 3.5
t = 3.640054945 + 3.5

Combine like terms: 3.640054945 + 3.5 = 7.140054945
t = 7.140054945

Simplifying
t = 7.140054945


Subproblem 2
t + -3.5 = -3.640054945

Simplifying
t + -3.5 = -3.640054945

Reorder the terms:
-3.5 + t = -3.640054945

Solving
-3.5 + t = -3.640054945

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 = -3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -3.640054945 + 3.5
t = -3.640054945 + 3.5

Combine like terms: -3.640054945 + 3.5 = -0.140054945
t = -0.140054945

Simplifying
t = -0.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.140054945, -0.140054945}
Solution
t = {7.140054945, -0.140054945}

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