64t^2+16t-1=0

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Solution for 64t^2+16t-1=0 equation: 


Simplifying
64t2 + 16t + -1 = 0

Reorder the terms:
-1 + 16t + 64t2 = 0

Solving
-1 + 16t + 64t2 = 0

Solving for variable 't'.

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

Divide each side by '64'.
-0.015625 + 0.25t + t2 = 0

Move the constant term to the right:

Add '0.015625' to each side of the equation.
-0.015625 + 0.25t + 0.015625 + t2 = 0 + 0.015625

Reorder the terms:
-0.015625 + 0.015625 + 0.25t + t2 = 0 + 0.015625

Combine like terms: -0.015625 + 0.015625 = 0.000000
0.000000 + 0.25t + t2 = 0 + 0.015625
0.25t + t2 = 0 + 0.015625

Combine like terms: 0 + 0.015625 = 0.015625
0.25t + t2 = 0.015625

The t term is 0.25t.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25t + 0.015625 + t2 = 0.015625 + 0.015625

Reorder the terms:
0.015625 + 0.25t + t2 = 0.015625 + 0.015625

Combine like terms: 0.015625 + 0.015625 = 0.03125
0.015625 + 0.25t + t2 = 0.03125

Factor a perfect square on the left side:
(t + 0.125)(t + 0.125) = 0.03125

Calculate the square root of the right side: 0.176776695

Break this problem into two subproblems by setting 
(t + 0.125) equal to 0.176776695 and -0.176776695.


Subproblem 1
t + 0.125 = 0.176776695

Simplifying
t + 0.125 = 0.176776695

Reorder the terms:
0.125 + t = 0.176776695

Solving
0.125 + t = 0.176776695

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = 0.176776695 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = 0.176776695 + -0.125
t = 0.176776695 + -0.125

Combine like terms: 0.176776695 + -0.125 = 0.051776695
t = 0.051776695

Simplifying
t = 0.051776695


Subproblem 2
t + 0.125 = -0.176776695

Simplifying
t + 0.125 = -0.176776695

Reorder the terms:
0.125 + t = -0.176776695

Solving
0.125 + t = -0.176776695

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = -0.176776695 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = -0.176776695 + -0.125
t = -0.176776695 + -0.125

Combine like terms: -0.176776695 + -0.125 = -0.301776695
t = -0.301776695

Simplifying
t = -0.301776695


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.051776695, -0.301776695}

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