(3x^2+x+1)-(2x^2-6-5)=1

Solution for (3x^2+x+1)-(2x^2-6-5)=1 equation:

Simplifying
(3x2 + x + 1) + -1(2x2 + -6 + -5) = 1

Reorder the terms:
(1 + x + 3x2) + -1(2x2 + -6 + -5) = 1

Remove parenthesis around (1 + x + 3x2)
1 + x + 3x2 + -1(2x2 + -6 + -5) = 1

Reorder the terms:
1 + x + 3x2 + -1(-6 + -5 + 2x2) = 1

Combine like terms: -6 + -5 = -11
1 + x + 3x2 + -1(-11 + 2x2) = 1
1 + x + 3x2 + (-11 * -1 + 2x2 * -1) = 1
1 + x + 3x2 + (11 + -2x2) = 1

Reorder the terms:
1 + 11 + x + 3x2 + -2x2 = 1

Combine like terms: 1 + 11 = 12
12 + x + 3x2 + -2x2 = 1

Combine like terms: 3x2 + -2x2 = 1x2
12 + x + 1x2 = 1

Solving
12 + x + 1x2 = 1

Solving for variable 'x'.

Reorder the terms:
12 + -1 + x + 1x2 = 1 + -1

Combine like terms: 12 + -1 = 11
11 + x + 1x2 = 1 + -1

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

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x + x2 = 0 + -11
x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
x + x2 = -11

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 = -11 + 0.25

Reorder the terms:
0.25 + x + x2 = -11 + 0.25

Combine like terms: -11 + 0.25 = -10.75
0.25 + x + x2 = -10.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -10.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.