0=9x^2+37x+22

Solution for 0=9x^2+37x+22 equation:

Simplifying
0 = 9x2 + 37x + 22

Reorder the terms:
0 = 22 + 37x + 9x2

Solving
0 = 22 + 37x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -22 = -22
-22 + -37x + -9x2 = 22 + 37x + 9x2 + -22 + -37x + -9x2

Reorder the terms:
-22 + -37x + -9x2 = 22 + -22 + 37x + -37x + 9x2 + -9x2

Combine like terms: 22 + -22 = 0
-22 + -37x + -9x2 = 0 + 37x + -37x + 9x2 + -9x2
-22 + -37x + -9x2 = 37x + -37x + 9x2 + -9x2

Combine like terms: 37x + -37x = 0
-22 + -37x + -9x2 = 0 + 9x2 + -9x2
-22 + -37x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-22 + -37x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(22 + 37x + 9x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(22 + 37x + 9x2)' equal to zero and attempt to solve:

Simplifying
22 + 37x + 9x2 = 0

Solving
22 + 37x + 9x2 = 0

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

Divide each side by '9'.
2.444444444 + 4.111111111x + x2 = 0

Move the constant term to the right:

Add '-2.444444444' to each side of the equation.
2.444444444 + 4.111111111x + -2.444444444 + x2 = 0 + -2.444444444

Reorder the terms:
2.444444444 + -2.444444444 + 4.111111111x + x2 = 0 + -2.444444444

Combine like terms: 2.444444444 + -2.444444444 = 0.000000000
0.000000000 + 4.111111111x + x2 = 0 + -2.444444444
4.111111111x + x2 = 0 + -2.444444444

Combine like terms: 0 + -2.444444444 = -2.444444444
4.111111111x + x2 = -2.444444444

The x term is 4.111111111x.  Take half its coefficient (2.055555556).
Square it (4.225308644) and add it to both sides.

Add '4.225308644' to each side of the equation.
4.111111111x + 4.225308644 + x2 = -2.444444444 + 4.225308644

Reorder the terms:
4.225308644 + 4.111111111x + x2 = -2.444444444 + 4.225308644

Combine like terms: -2.444444444 + 4.225308644 = 1.7808642
4.225308644 + 4.111111111x + x2 = 1.7808642

Factor a perfect square on the left side:
(x + 2.055555556)(x + 2.055555556) = 1.7808642

Calculate the square root of the right side: 1.33449024

Break this problem into two subproblems by setting 
(x + 2.055555556) equal to 1.33449024 and -1.33449024.

Subproblem 1
x + 2.055555556 = 1.33449024

Simplifying
x + 2.055555556 = 1.33449024

Reorder the terms:
2.055555556 + x = 1.33449024

Solving
2.055555556 + x = 1.33449024

Solving for variable 'x'.

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

Add '-2.055555556' to each side of the equation.
2.055555556 + -2.055555556 + x = 1.33449024 + -2.055555556

Combine like terms: 2.055555556 + -2.055555556 = 0.000000000
0.000000000 + x = 1.33449024 + -2.055555556
x = 1.33449024 + -2.055555556

Combine like terms: 1.33449024 + -2.055555556 = -0.721065316
x = -0.721065316

Simplifying
x = -0.721065316

Subproblem 2
x + 2.055555556 = -1.33449024

Simplifying
x + 2.055555556 = -1.33449024

Reorder the terms:
2.055555556 + x = -1.33449024

Solving
2.055555556 + x = -1.33449024

Solving for variable 'x'.

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

Add '-2.055555556' to each side of the equation.
2.055555556 + -2.055555556 + x = -1.33449024 + -2.055555556

Combine like terms: 2.055555556 + -2.055555556 = 0.000000000
0.000000000 + x = -1.33449024 + -2.055555556
x = -1.33449024 + -2.055555556

Combine like terms: -1.33449024 + -2.055555556 = -3.390045796
x = -3.390045796

Simplifying
x = -3.390045796

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.721065316, -3.390045796}
Solution
x = {-0.721065316, -3.390045796}