1=3-t^2+9t-.75

Solution for 1=3-t^2+9t-.75 equation:

Simplifying
1 = 3 + -1t2 + 9t + -0.75

Reorder the terms:
1 = 3 + -0.75 + 9t + -1t2

Combine like terms: 3 + -0.75 = 2.25
1 = 2.25 + 9t + -1t2

Solving
1 = 2.25 + 9t + -1t2

Solving for variable 't'.

Combine like terms: 1 + -2.25 = -1.25
-1.25 + -9t + t2 = 2.25 + 9t + -1t2 + -2.25 + -9t + t2

Reorder the terms:
-1.25 + -9t + t2 = 2.25 + -2.25 + 9t + -9t + -1t2 + t2

Combine like terms: 2.25 + -2.25 = 0.00
-1.25 + -9t + t2 = 0.00 + 9t + -9t + -1t2 + t2
-1.25 + -9t + t2 = 9t + -9t + -1t2 + t2

Combine like terms: 9t + -9t = 0
-1.25 + -9t + t2 = 0 + -1t2 + t2
-1.25 + -9t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-1.25 + -9t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -9t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -9t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -9t + t2 = 0 + 1.25
-9t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-9t + t2 = 1.25

The t term is -9t.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9t + 20.25 + t2 = 1.25 + 20.25

Reorder the terms:
20.25 + -9t + t2 = 1.25 + 20.25

Combine like terms: 1.25 + 20.25 = 21.5
20.25 + -9t + t2 = 21.5

Factor a perfect square on the left side:
(t + -4.5)(t + -4.5) = 21.5

Calculate the square root of the right side: 4.636809248

Break this problem into two subproblems by setting 
(t + -4.5) equal to 4.636809248 and -4.636809248.

Subproblem 1
t + -4.5 = 4.636809248

Simplifying
t + -4.5 = 4.636809248

Reorder the terms:
-4.5 + t = 4.636809248

Solving
-4.5 + t = 4.636809248

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = 4.636809248 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = 4.636809248 + 4.5
t = 4.636809248 + 4.5

Combine like terms: 4.636809248 + 4.5 = 9.136809248
t = 9.136809248

Simplifying
t = 9.136809248

Subproblem 2
t + -4.5 = -4.636809248

Simplifying
t + -4.5 = -4.636809248

Reorder the terms:
-4.5 + t = -4.636809248

Solving
-4.5 + t = -4.636809248

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = -4.636809248 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = -4.636809248 + 4.5
t = -4.636809248 + 4.5

Combine like terms: -4.636809248 + 4.5 = -0.136809248
t = -0.136809248

Simplifying
t = -0.136809248

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.136809248, -0.136809248}