x=18x^2+21x-22

Solution for x=18x^2+21x-22 equation:

Simplifying
x = 18x2 + 21x + -22

Reorder the terms:
x = -22 + 21x + 18x2

Solving
x = -22 + 21x + 18x2

Solving for variable 'x'.

Reorder the terms:
22 + x + -21x + -18x2 = -22 + 21x + 18x2 + 22 + -21x + -18x2

Combine like terms: x + -21x = -20x
22 + -20x + -18x2 = -22 + 21x + 18x2 + 22 + -21x + -18x2

Reorder the terms:
22 + -20x + -18x2 = -22 + 22 + 21x + -21x + 18x2 + -18x2

Combine like terms: -22 + 22 = 0
22 + -20x + -18x2 = 0 + 21x + -21x + 18x2 + -18x2
22 + -20x + -18x2 = 21x + -21x + 18x2 + -18x2

Combine like terms: 21x + -21x = 0
22 + -20x + -18x2 = 0 + 18x2 + -18x2
22 + -20x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
22 + -20x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -10x + -9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + -10x + -9x2)' equal to zero and attempt to solve:

Simplifying
11 + -10x + -9x2 = 0

Solving
11 + -10x + -9x2 = 0

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

Divide each side by '-9'.
-1.222222222 + 1.111111111x + x2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + 1.111111111x + 1.222222222 + x2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + 1.111111111x + x2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + 1.111111111x + x2 = 0 + 1.222222222
1.111111111x + x2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
1.111111111x + x2 = 1.222222222

The x term is 1.111111111x.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111x + 0.3086419752 + x2 = 1.222222222 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111x + x2 = 1.222222222 + 0.3086419752

Combine like terms: 1.222222222 + 0.3086419752 = 1.5308641972
0.3086419752 + 1.111111111x + x2 = 1.5308641972

Factor a perfect square on the left side:
(x + 0.5555555555)(x + 0.5555555555) = 1.5308641972

Calculate the square root of the right side: 1.237280969

Break this problem into two subproblems by setting 
(x + 0.5555555555) equal to 1.237280969 and -1.237280969.

Subproblem 1
x + 0.5555555555 = 1.237280969

Simplifying
x + 0.5555555555 = 1.237280969

Reorder the terms:
0.5555555555 + x = 1.237280969

Solving
0.5555555555 + x = 1.237280969

Solving for variable 'x'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + x = 1.237280969 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + x = 1.237280969 + -0.5555555555
x = 1.237280969 + -0.5555555555

Combine like terms: 1.237280969 + -0.5555555555 = 0.6817254135
x = 0.6817254135

Simplifying
x = 0.6817254135

Subproblem 2
x + 0.5555555555 = -1.237280969

Simplifying
x + 0.5555555555 = -1.237280969

Reorder the terms:
0.5555555555 + x = -1.237280969

Solving
0.5555555555 + x = -1.237280969

Solving for variable 'x'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + x = -1.237280969 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + x = -1.237280969 + -0.5555555555
x = -1.237280969 + -0.5555555555

Combine like terms: -1.237280969 + -0.5555555555 = -1.7928365245
x = -1.7928365245

Simplifying
x = -1.7928365245

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6817254135, -1.7928365245}
Solution
x = {0.6817254135, -1.7928365245}