5x^2+33x+22=x+6

Solution for 5x^2+33x+22=x+6 equation:

Simplifying
5x2 + 33x + 22 = x + 6

Reorder the terms:
22 + 33x + 5x2 = x + 6

Reorder the terms:
22 + 33x + 5x2 = 6 + x

Solving
22 + 33x + 5x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
22 + -6 + 33x + -1x + 5x2 = 6 + x + -6 + -1x

Combine like terms: 22 + -6 = 16
16 + 33x + -1x + 5x2 = 6 + x + -6 + -1x

Combine like terms: 33x + -1x = 32x
16 + 32x + 5x2 = 6 + x + -6 + -1x

Reorder the terms:
16 + 32x + 5x2 = 6 + -6 + x + -1x

Combine like terms: 6 + -6 = 0
16 + 32x + 5x2 = 0 + x + -1x
16 + 32x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
16 + 32x + 5x2 = 0

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

Divide each side by '5'.
3.2 + 6.4x + x2 = 0

Move the constant term to the right:

Add '-3.2' to each side of the equation.
3.2 + 6.4x + -3.2 + x2 = 0 + -3.2

Reorder the terms:
3.2 + -3.2 + 6.4x + x2 = 0 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + 6.4x + x2 = 0 + -3.2
6.4x + x2 = 0 + -3.2

Combine like terms: 0 + -3.2 = -3.2
6.4x + x2 = -3.2

The x term is 6.4x.  Take half its coefficient (3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
6.4x + 10.24 + x2 = -3.2 + 10.24

Reorder the terms:
10.24 + 6.4x + x2 = -3.2 + 10.24

Combine like terms: -3.2 + 10.24 = 7.04
10.24 + 6.4x + x2 = 7.04

Factor a perfect square on the left side:
(x + 3.2)(x + 3.2) = 7.04

Calculate the square root of the right side: 2.653299832

Break this problem into two subproblems by setting 
(x + 3.2) equal to 2.653299832 and -2.653299832.

Subproblem 1
x + 3.2 = 2.653299832

Simplifying
x + 3.2 = 2.653299832

Reorder the terms:
3.2 + x = 2.653299832

Solving
3.2 + x = 2.653299832

Solving for variable 'x'.

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

Add '-3.2' to each side of the equation.
3.2 + -3.2 + x = 2.653299832 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + x = 2.653299832 + -3.2
x = 2.653299832 + -3.2

Combine like terms: 2.653299832 + -3.2 = -0.546700168
x = -0.546700168

Simplifying
x = -0.546700168

Subproblem 2
x + 3.2 = -2.653299832

Simplifying
x + 3.2 = -2.653299832

Reorder the terms:
3.2 + x = -2.653299832

Solving
3.2 + x = -2.653299832

Solving for variable 'x'.

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

Add '-3.2' to each side of the equation.
3.2 + -3.2 + x = -2.653299832 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + x = -2.653299832 + -3.2
x = -2.653299832 + -3.2

Combine like terms: -2.653299832 + -3.2 = -5.853299832
x = -5.853299832

Simplifying
x = -5.853299832

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.546700168, -5.853299832}