-16t^2+24t-1=0

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Solution for -16t^2+24t-1=0 equation: 


Simplifying
-16t2 + 24t + -1 = 0

Reorder the terms:
-1 + 24t + -16t2 = 0

Solving
-1 + 24t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.0625 + -1.5t + t2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -1.5t + -0.0625 + t2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -1.5t + t2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -1.5t + t2 = 0 + -0.0625
-1.5t + t2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-1.5t + t2 = -0.0625

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 = -0.0625 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = -0.0625 + 0.5625

Combine like terms: -0.0625 + 0.5625 = 0.5
0.5625 + -1.5t + t2 = 0.5

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(t + -0.75) equal to 0.707106781 and -0.707106781.


Subproblem 1
t + -0.75 = 0.707106781

Simplifying
t + -0.75 = 0.707106781

Reorder the terms:
-0.75 + t = 0.707106781

Solving
-0.75 + t = 0.707106781

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 = 0.707106781 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 0.707106781 + 0.75
t = 0.707106781 + 0.75

Combine like terms: 0.707106781 + 0.75 = 1.457106781
t = 1.457106781

Simplifying
t = 1.457106781


Subproblem 2
t + -0.75 = -0.707106781

Simplifying
t + -0.75 = -0.707106781

Reorder the terms:
-0.75 + t = -0.707106781

Solving
-0.75 + t = -0.707106781

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 = -0.707106781 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -0.707106781 + 0.75
t = -0.707106781 + 0.75

Combine like terms: -0.707106781 + 0.75 = 0.042893219
t = 0.042893219

Simplifying
t = 0.042893219


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.457106781, 0.042893219}

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