-0.25t^2+t+3=0

Solution for -0.25t^2+t+3=0 equation:

Simplifying
-0.25t2 + t + 3 = 0

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

Solving
3 + t + -0.25t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
-12 + -4t + t2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -4t + 12 + t2 = 0 + 12

Reorder the terms:
-12 + 12 + -4t + t2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -4t + t2 = 0 + 12
-4t + t2 = 0 + 12

Combine like terms: 0 + 12 = 12
-4t + t2 = 12

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

Add '0.25' to each side of the equation.
-4t + 0.25 + t2 = 12 + 0.25

Reorder the terms:
0.25 + -4t + t2 = 12 + 0.25

Combine like terms: 12 + 0.25 = 12.25
0.25 + -4t + t2 = 12.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(t + 0.5) equal to 3.5 and -3.5.

Subproblem 1
t + 0.5 = 3.5

Simplifying
t + 0.5 = 3.5

Reorder the terms:
0.5 + t = 3.5

Solving
0.5 + t = 3.5

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 3.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 3.5 + -0.5
t = 3.5 + -0.5

Combine like terms: 3.5 + -0.5 = 3
t = 3

Simplifying
t = 3

Subproblem 2
t + 0.5 = -3.5

Simplifying
t + 0.5 = -3.5

Reorder the terms:
0.5 + t = -3.5

Solving
0.5 + t = -3.5

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -3.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -3.5 + -0.5
t = -3.5 + -0.5

Combine like terms: -3.5 + -0.5 = -4
t = -4

Simplifying
t = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3, -4}