2t^2-t-3=1

Solution for 2t^2-t-3=1 equation:

Simplifying
2t2 + -1t + -3 = 1

Reorder the terms:
-3 + -1t + 2t2 = 1

Solving
-3 + -1t + 2t2 = 1

Solving for variable 't'.

Reorder the terms:
-3 + -1 + -1t + 2t2 = 1 + -1

Combine like terms: -3 + -1 = -4
-4 + -1t + 2t2 = 1 + -1

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

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

Divide each side by '2'.
-2 + -0.5t + t2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.5t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.5t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.5t + t2 = 0 + 2
-0.5t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.5t + t2 = 2

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 = 2 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + -0.5t + t2 = 2.0625

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(t + -0.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
t + -0.25 = 1.436140662

Simplifying
t + -0.25 = 1.436140662

Reorder the terms:
-0.25 + t = 1.436140662

Solving
-0.25 + t = 1.436140662

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 = 1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = 1.436140662 + 0.25
t = 1.436140662 + 0.25

Combine like terms: 1.436140662 + 0.25 = 1.686140662
t = 1.686140662

Simplifying
t = 1.686140662

Subproblem 2
t + -0.25 = -1.436140662

Simplifying
t + -0.25 = -1.436140662

Reorder the terms:
-0.25 + t = -1.436140662

Solving
-0.25 + t = -1.436140662

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 = -1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = -1.436140662 + 0.25
t = -1.436140662 + 0.25

Combine like terms: -1.436140662 + 0.25 = -1.186140662
t = -1.186140662

Simplifying
t = -1.186140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.686140662, -1.186140662}