x^2+9x=6

Solution for x^2+9x=6 equation:

Simplifying
x2 + 9x = 6

Reorder the terms:
9x + x2 = 6

Solving
9x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 9x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 9x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 9x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 9x + x2 = 0 + 6
9x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
9x + x2 = 6

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 6 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 6 + 20.25

Combine like terms: 6 + 20.25 = 26.25
20.25 + 9x + x2 = 26.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
x + 4.5 = 5.123475383

Simplifying
x + 4.5 = 5.123475383

Reorder the terms:
4.5 + x = 5.123475383

Solving
4.5 + x = 5.123475383

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.123475383 + -4.5
x = 5.123475383 + -4.5

Combine like terms: 5.123475383 + -4.5 = 0.623475383
x = 0.623475383

Simplifying
x = 0.623475383

Subproblem 2
x + 4.5 = -5.123475383

Simplifying
x + 4.5 = -5.123475383

Reorder the terms:
4.5 + x = -5.123475383

Solving
4.5 + x = -5.123475383

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.123475383 + -4.5
x = -5.123475383 + -4.5

Combine like terms: -5.123475383 + -4.5 = -9.623475383
x = -9.623475383

Simplifying
x = -9.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.623475383, -9.623475383}