0=-16t^2-128t-144

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Solution for 0=-16t^2-128t-144 equation: 


Simplifying
0 = -16t2 + -128t + -144

Reorder the terms:
0 = -144 + -128t + -16t2

Solving
0 = -144 + -128t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 144 = 144
144 + 128t + 16t2 = -144 + -128t + -16t2 + 144 + 128t + 16t2

Reorder the terms:
144 + 128t + 16t2 = -144 + 144 + -128t + 128t + -16t2 + 16t2

Combine like terms: -144 + 144 = 0
144 + 128t + 16t2 = 0 + -128t + 128t + -16t2 + 16t2
144 + 128t + 16t2 = -128t + 128t + -16t2 + 16t2

Combine like terms: -128t + 128t = 0
144 + 128t + 16t2 = 0 + -16t2 + 16t2
144 + 128t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
144 + 128t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(9 + 8t + t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(9 + 8t + t2)' equal to zero and attempt to solve:

Simplifying
9 + 8t + t2 = 0

Solving
9 + 8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 8t + -9 + t2 = 0 + -9

Reorder the terms:
9 + -9 + 8t + t2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8t + t2 = 0 + -9
8t + t2 = 0 + -9

Combine like terms: 0 + -9 = -9
8t + t2 = -9

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = -9 + 16

Reorder the terms:
16 + 8t + t2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + 8t + t2 = 7

Factor a perfect square on the left side:
(t + 4)(t + 4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + 4) equal to 2.645751311 and -2.645751311.


Subproblem 1
t + 4 = 2.645751311

Simplifying
t + 4 = 2.645751311

Reorder the terms:
4 + t = 2.645751311

Solving
4 + t = 2.645751311

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + t = 2.645751311 + -4
t = 2.645751311 + -4

Combine like terms: 2.645751311 + -4 = -1.354248689
t = -1.354248689

Simplifying
t = -1.354248689


Subproblem 2
t + 4 = -2.645751311

Simplifying
t + 4 = -2.645751311

Reorder the terms:
4 + t = -2.645751311

Solving
4 + t = -2.645751311

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + t = -2.645751311 + -4
t = -2.645751311 + -4

Combine like terms: -2.645751311 + -4 = -6.645751311
t = -6.645751311

Simplifying
t = -6.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.354248689, -6.645751311}
Solution
t = {-1.354248689, -6.645751311}

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