4t^2=2t+1

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

Simplifying
4t2 = 2t + 1

Reorder the terms:
4t2 = 1 + 2t

Solving
4t2 = 1 + 2t

Solving for variable 't'.

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

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

Combine like terms: 1 + -1 = 0
-1 + -2t + 4t2 = 0 + 2t + -2t
-1 + -2t + 4t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-1 + -2t + 4t2 = 0

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 = 0.809016994
t = 0.809016994

Simplifying
t = 0.809016994

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 = -0.309016994
t = -0.309016994

Simplifying
t = -0.309016994

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