(-16(t^2))-(2t)+1=0

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


Simplifying
(-16(t2)) + -1(2t) + 1 = 0

Remove parenthesis around (2t)
(-16t2) + -1 * 2t + 1 = 0

Multiply -1 * 2
(-16t2) + -2t + 1 = 0

Reorder the terms:
1 + -2t + (-16t2) = 0

Solving
1 + -2t + (-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 + 0.125t + t2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + 0.125t + 0.0625 + t2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + 0.125t + t2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + 0.125t + t2 = 0 + 0.0625
0.125t + t2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
0.125t + t2 = 0.0625

The t term is 0.125t.  Take half its coefficient (0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
0.125t + 0.00390625 + t2 = 0.0625 + 0.00390625

Reorder the terms:
0.00390625 + 0.125t + t2 = 0.0625 + 0.00390625

Combine like terms: 0.0625 + 0.00390625 = 0.06640625
0.00390625 + 0.125t + t2 = 0.06640625

Factor a perfect square on the left side:
((t) + 0.0625)((t) + 0.0625) = 0.06640625

Calculate the square root of the right side: 0.257694102

Break this problem into two subproblems by setting 
((t) + 0.0625) equal to 0.257694102 and -0.257694102.

Subproblem 1

(t) + 0.0625 = 0.257694102 Simplifying (t) + 0.0625 = 0.257694102 t + 0.0625 = 0.257694102 Reorder the terms: 0.0625 + t = 0.257694102 Solving 0.0625 + t = 0.257694102 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + t = 0.257694102 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + t = 0.257694102 + -0.0625 t = 0.257694102 + -0.0625 Combine like terms: 0.257694102 + -0.0625 = 0.195194102 t = 0.195194102 Simplifying t = 0.195194102

Subproblem 2

(t) + 0.0625 = -0.257694102 Simplifying (t) + 0.0625 = -0.257694102 t + 0.0625 = -0.257694102 Reorder the terms: 0.0625 + t = -0.257694102 Solving 0.0625 + t = -0.257694102 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + t = -0.257694102 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + t = -0.257694102 + -0.0625 t = -0.257694102 + -0.0625 Combine like terms: -0.257694102 + -0.0625 = -0.320194102 t = -0.320194102 Simplifying t = -0.320194102

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.195194102, -0.320194102}

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