3.4=6-x-x^2

Solution for 3.4=6-x-x^2 equation:

Simplifying
3.4 = 6 + -1x + -1x2

Solving
3.4 = 6 + -1x + -1x2

Solving for variable 'x'.

Combine like terms: 3.4 + -6 = -2.6
-2.6 + x + x2 = 6 + -1x + -1x2 + -6 + x + x2

Reorder the terms:
-2.6 + x + x2 = 6 + -6 + -1x + x + -1x2 + x2

Combine like terms: 6 + -6 = 0
-2.6 + x + x2 = 0 + -1x + x + -1x2 + x2
-2.6 + x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-2.6 + x + x2 = 0 + -1x2 + x2
-2.6 + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2.6 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + x + 2.6 + x2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + x + x2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + x + x2 = 0 + 2.6
x + x2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
x + x2 = 2.6

The x term is x.  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.
x + 0.25 + x2 = 2.6 + 0.25

Reorder the terms:
0.25 + x + x2 = 2.6 + 0.25

Combine like terms: 2.6 + 0.25 = 2.85
0.25 + x + x2 = 2.85

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.85

Calculate the square root of the right side: 1.688194302

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.688194302 and -1.688194302.

Subproblem 1
x + 0.5 = 1.688194302

Simplifying
x + 0.5 = 1.688194302

Reorder the terms:
0.5 + x = 1.688194302

Solving
0.5 + x = 1.688194302

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.688194302 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.688194302 + -0.5
x = 1.688194302 + -0.5

Combine like terms: 1.688194302 + -0.5 = 1.188194302
x = 1.188194302

Simplifying
x = 1.188194302

Subproblem 2
x + 0.5 = -1.688194302

Simplifying
x + 0.5 = -1.688194302

Reorder the terms:
0.5 + x = -1.688194302

Solving
0.5 + x = -1.688194302

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.688194302 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.688194302 + -0.5
x = -1.688194302 + -0.5

Combine like terms: -1.688194302 + -0.5 = -2.188194302
x = -2.188194302

Simplifying
x = -2.188194302

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.188194302, -2.188194302}