16t^2-24t+4=0

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Solution for 16t^2-24t+4=0 equation: 


Simplifying
16t2 + -24t + 4 = 0

Reorder the terms:
4 + -24t + 16t2 = 0

Solving
4 + -24t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -6t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -6t + 4t2)' equal to zero and attempt to solve:

Simplifying
1 + -6t + 4t2 = 0

Solving
1 + -6t + 4t2 = 0

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

Divide each side by '4'.
0.25 + -1.5t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.5t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.5t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.5t + t2 = 0 + -0.25
-1.5t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.5t + t2 = -0.25

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = -0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = -0.25 + 0.5625

Combine like terms: -0.25 + 0.5625 = 0.3125
0.5625 + -1.5t + t2 = 0.3125

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(t + -0.75) equal to 0.559016994 and -0.559016994.


Subproblem 1
t + -0.75 = 0.559016994

Simplifying
t + -0.75 = 0.559016994

Reorder the terms:
-0.75 + t = 0.559016994

Solving
-0.75 + t = 0.559016994

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 0.559016994 + 0.75
t = 0.559016994 + 0.75

Combine like terms: 0.559016994 + 0.75 = 1.309016994
t = 1.309016994

Simplifying
t = 1.309016994


Subproblem 2
t + -0.75 = -0.559016994

Simplifying
t + -0.75 = -0.559016994

Reorder the terms:
-0.75 + t = -0.559016994

Solving
-0.75 + t = -0.559016994

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -0.559016994 + 0.75
t = -0.559016994 + 0.75

Combine like terms: -0.559016994 + 0.75 = 0.190983006
t = 0.190983006

Simplifying
t = 0.190983006


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.309016994, 0.190983006}
Solution
t = {1.309016994, 0.190983006}

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