-16t^2-18t+24=0

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Solution for -16t^2-18t+24=0 equation: 


Simplifying
-16t2 + -18t + 24 = 0

Reorder the terms:
24 + -18t + -16t2 = 0

Solving
24 + -18t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -9t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + -9t + -8t2)' equal to zero and attempt to solve:

Simplifying
12 + -9t + -8t2 = 0

Solving
12 + -9t + -8t2 = 0

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

Divide each side by '-8'.
-1.5 + 1.125t + t2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.125t + 1.5 + t2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.125t + t2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.125t + t2 = 0 + 1.5
1.125t + t2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.125t + t2 = 1.5

The t term is 1.125t.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125t + 0.31640625 + t2 = 1.5 + 0.31640625

Reorder the terms:
0.31640625 + 1.125t + t2 = 1.5 + 0.31640625

Combine like terms: 1.5 + 0.31640625 = 1.81640625
0.31640625 + 1.125t + t2 = 1.81640625

Factor a perfect square on the left side:
(t + 0.5625)(t + 0.5625) = 1.81640625

Calculate the square root of the right side: 1.347741166

Break this problem into two subproblems by setting 
(t + 0.5625) equal to 1.347741166 and -1.347741166.


Subproblem 1
t + 0.5625 = 1.347741166

Simplifying
t + 0.5625 = 1.347741166

Reorder the terms:
0.5625 + t = 1.347741166

Solving
0.5625 + t = 1.347741166

Solving for variable 't'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + t = 1.347741166 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + t = 1.347741166 + -0.5625
t = 1.347741166 + -0.5625

Combine like terms: 1.347741166 + -0.5625 = 0.785241166
t = 0.785241166

Simplifying
t = 0.785241166


Subproblem 2
t + 0.5625 = -1.347741166

Simplifying
t + 0.5625 = -1.347741166

Reorder the terms:
0.5625 + t = -1.347741166

Solving
0.5625 + t = -1.347741166

Solving for variable 't'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + t = -1.347741166 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + t = -1.347741166 + -0.5625
t = -1.347741166 + -0.5625

Combine like terms: -1.347741166 + -0.5625 = -1.910241166
t = -1.910241166

Simplifying
t = -1.910241166


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.785241166, -1.910241166}
Solution
t = {0.785241166, -1.910241166}

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