4t^2+2t-1=0

Solution for 4t^2+2t-1=0 equation:

Simplifying
4t2 + 2t + -1 = 0

Reorder the terms:
-1 + 2t + 4t2 = 0

Solving
-1 + 2t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
-0.25 + 0.5t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.5t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.5t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.5t + t2 = 0 + 0.25
0.5t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.5t + t2 = 0.25

The t term is 0.5t.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5t + 0.0625 + t2 = 0.25 + 0.0625

Reorder the terms:
0.0625 + 0.5t + t2 = 0.25 + 0.0625

Combine like terms: 0.25 + 0.0625 = 0.3125
0.0625 + 0.5t + t2 = 0.3125

Factor a perfect square on the left side:
(t + 0.25)(t + 0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(t + 0.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
t + 0.25 = 0.559016994

Simplifying
t + 0.25 = 0.559016994

Reorder the terms:
0.25 + t = 0.559016994

Solving
0.25 + t = 0.559016994

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = 0.559016994 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = 0.559016994 + -0.25
t = 0.559016994 + -0.25

Combine like terms: 0.559016994 + -0.25 = 0.309016994
t = 0.309016994

Simplifying
t = 0.309016994

Subproblem 2
t + 0.25 = -0.559016994

Simplifying
t + 0.25 = -0.559016994

Reorder the terms:
0.25 + t = -0.559016994

Solving
0.25 + t = -0.559016994

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = -0.559016994 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = -0.559016994 + -0.25
t = -0.559016994 + -0.25

Combine like terms: -0.559016994 + -0.25 = -0.809016994
t = -0.809016994

Simplifying
t = -0.809016994

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.309016994, -0.809016994}