-t^2+2t+2=

Solution for -t^2+2t+2= equation:

Simplifying
-1t2 + 2t + 2 = 0

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

Solving
2 + 2t + -1t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -2t + t2 = 0

Move the constant term to the right:

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

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

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

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

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 2 + 1

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

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

Factor a perfect square on the left side:
(t + -1)(t + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(t + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
t + -1 = 1.732050808

Simplifying
t + -1 = 1.732050808

Reorder the terms:
-1 + t = 1.732050808

Solving
-1 + t = 1.732050808

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + t = 1.732050808 + 1
t = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
t = 2.732050808

Simplifying
t = 2.732050808

Subproblem 2
t + -1 = -1.732050808

Simplifying
t + -1 = -1.732050808

Reorder the terms:
-1 + t = -1.732050808

Solving
-1 + t = -1.732050808

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + t = -1.732050808 + 1
t = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
t = -0.732050808

Simplifying
t = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.732050808, -0.732050808}