=(-9x^2+3)+(x+1)

Solution for =(-9x^2+3)+(x+1) equation:

Simplifying
0 = (-9x2 + 3) + (x + 1)

Reorder the terms:
0 = (3 + -9x2) + (x + 1)

Remove parenthesis around (3 + -9x2)
0 = 3 + -9x2 + (x + 1)

Reorder the terms:
0 = 3 + -9x2 + (1 + x)

Remove parenthesis around (1 + x)
0 = 3 + -9x2 + 1 + x

Reorder the terms:
0 = 3 + 1 + x + -9x2

Combine like terms: 3 + 1 = 4
0 = 4 + x + -9x2

Solving
0 = 4 + x + -9x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -1x + 9x2 = 4 + x + -9x2 + -4 + -1x + 9x2

Reorder the terms:
-4 + -1x + 9x2 = 4 + -4 + x + -1x + -9x2 + 9x2

Combine like terms: 4 + -4 = 0
-4 + -1x + 9x2 = 0 + x + -1x + -9x2 + 9x2
-4 + -1x + 9x2 = x + -1x + -9x2 + 9x2

Combine like terms: x + -1x = 0
-4 + -1x + 9x2 = 0 + -9x2 + 9x2
-4 + -1x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-4 + -1x + 9x2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.1111111111x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.1111111111x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.1111111111x + x2 = 0 + 0.4444444444
-0.1111111111x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.1111111111x + x2 = 0.4444444444

The x term is -0.1111111111x.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111x + 0.003086419752 + x2 = 0.4444444444 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111x + x2 = 0.4444444444 + 0.003086419752

Combine like terms: 0.4444444444 + 0.003086419752 = 0.447530864152
0.003086419752 + -0.1111111111x + x2 = 0.447530864152

Factor a perfect square on the left side:
(x + -0.05555555555)(x + -0.05555555555) = 0.447530864152

Calculate the square root of the right side: 0.668977477

Break this problem into two subproblems by setting 
(x + -0.05555555555) equal to 0.668977477 and -0.668977477.

Subproblem 1
x + -0.05555555555 = 0.668977477

Simplifying
x + -0.05555555555 = 0.668977477

Reorder the terms:
-0.05555555555 + x = 0.668977477

Solving
-0.05555555555 + x = 0.668977477

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = 0.668977477 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = 0.668977477 + 0.05555555555
x = 0.668977477 + 0.05555555555

Combine like terms: 0.668977477 + 0.05555555555 = 0.72453303255
x = 0.72453303255

Simplifying
x = 0.72453303255

Subproblem 2
x + -0.05555555555 = -0.668977477

Simplifying
x + -0.05555555555 = -0.668977477

Reorder the terms:
-0.05555555555 + x = -0.668977477

Solving
-0.05555555555 + x = -0.668977477

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = -0.668977477 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = -0.668977477 + 0.05555555555
x = -0.668977477 + 0.05555555555

Combine like terms: -0.668977477 + 0.05555555555 = -0.61342192145
x = -0.61342192145

Simplifying
x = -0.61342192145

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.72453303255, -0.61342192145}