4.9t^2-2t-1=0

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Solution for 4.9t^2-2t-1=0 equation:


Simplifying
4.9t2 + -2t + -1 = 0

Reorder the terms:
-1 + -2t + 4.9t2 = 0

Solving
-1 + -2t + 4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '4.9'.
-0.2040816327 + -0.4081632653t + t2 = 0

Move the constant term to the right:

Add '0.2040816327' to each side of the equation.
-0.2040816327 + -0.4081632653t + 0.2040816327 + t2 = 0 + 0.2040816327

Reorder the terms:
-0.2040816327 + 0.2040816327 + -0.4081632653t + t2 = 0 + 0.2040816327

Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000
0.0000000000 + -0.4081632653t + t2 = 0 + 0.2040816327
-0.4081632653t + t2 = 0 + 0.2040816327

Combine like terms: 0 + 0.2040816327 = 0.2040816327
-0.4081632653t + t2 = 0.2040816327

The t term is -0.4081632653t.  Take half its coefficient (-0.2040816327).
Square it (0.04164931281) and add it to both sides.

Add '0.04164931281' to each side of the equation.
-0.4081632653t + 0.04164931281 + t2 = 0.2040816327 + 0.04164931281

Reorder the terms:
0.04164931281 + -0.4081632653t + t2 = 0.2040816327 + 0.04164931281

Combine like terms: 0.2040816327 + 0.04164931281 = 0.24573094551
0.04164931281 + -0.4081632653t + t2 = 0.24573094551

Factor a perfect square on the left side:
(t + -0.2040816327)(t + -0.2040816327) = 0.24573094551

Calculate the square root of the right side: 0.495712563

Break this problem into two subproblems by setting 
(t + -0.2040816327) equal to 0.495712563 and -0.495712563.

Subproblem 1

t + -0.2040816327 = 0.495712563 Simplifying t + -0.2040816327 = 0.495712563 Reorder the terms: -0.2040816327 + t = 0.495712563 Solving -0.2040816327 + t = 0.495712563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = 0.495712563 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 0.495712563 + 0.2040816327 t = 0.495712563 + 0.2040816327 Combine like terms: 0.495712563 + 0.2040816327 = 0.6997941957 t = 0.6997941957 Simplifying t = 0.6997941957

Subproblem 2

t + -0.2040816327 = -0.495712563 Simplifying t + -0.2040816327 = -0.495712563 Reorder the terms: -0.2040816327 + t = -0.495712563 Solving -0.2040816327 + t = -0.495712563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = -0.495712563 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -0.495712563 + 0.2040816327 t = -0.495712563 + 0.2040816327 Combine like terms: -0.495712563 + 0.2040816327 = -0.2916309303 t = -0.2916309303 Simplifying t = -0.2916309303

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.6997941957, -0.2916309303}

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