22x*x=-9-99x

Solution for 22x*x=-9-99x equation:

Simplifying
22x * x = -9 + -99x

Multiply x * x
22x2 = -9 + -99x

Solving
22x2 = -9 + -99x

Solving for variable 'x'.

Reorder the terms:
9 + 99x + 22x2 = -9 + -99x + 9 + 99x

Reorder the terms:
9 + 99x + 22x2 = -9 + 9 + -99x + 99x

Combine like terms: -9 + 9 = 0
9 + 99x + 22x2 = 0 + -99x + 99x
9 + 99x + 22x2 = -99x + 99x

Combine like terms: -99x + 99x = 0
9 + 99x + 22x2 = 0

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

Divide each side by '22'.
0.4090909091 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-0.4090909091' to each side of the equation.
0.4090909091 + 4.5x + -0.4090909091 + x2 = 0 + -0.4090909091

Reorder the terms:
0.4090909091 + -0.4090909091 + 4.5x + x2 = 0 + -0.4090909091

Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000
0.0000000000 + 4.5x + x2 = 0 + -0.4090909091
4.5x + x2 = 0 + -0.4090909091

Combine like terms: 0 + -0.4090909091 = -0.4090909091
4.5x + x2 = -0.4090909091

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -0.4090909091 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -0.4090909091 + 5.0625

Combine like terms: -0.4090909091 + 5.0625 = 4.6534090909
5.0625 + 4.5x + x2 = 4.6534090909

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 4.6534090909

Calculate the square root of the right side: 2.157176184

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.157176184 and -2.157176184.

Subproblem 1
x + 2.25 = 2.157176184

Simplifying
x + 2.25 = 2.157176184

Reorder the terms:
2.25 + x = 2.157176184

Solving
2.25 + x = 2.157176184

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.157176184 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.157176184 + -2.25
x = 2.157176184 + -2.25

Combine like terms: 2.157176184 + -2.25 = -0.092823816
x = -0.092823816

Simplifying
x = -0.092823816

Subproblem 2
x + 2.25 = -2.157176184

Simplifying
x + 2.25 = -2.157176184

Reorder the terms:
2.25 + x = -2.157176184

Solving
2.25 + x = -2.157176184

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.157176184 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.157176184 + -2.25
x = -2.157176184 + -2.25

Combine like terms: -2.157176184 + -2.25 = -4.407176184
x = -4.407176184

Simplifying
x = -4.407176184

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.092823816, -4.407176184}