Solve by completing the square:

x^2+9x+6=0

To solve the quadratic equation x^2 + 9x + 6 = 0 by completing the square, follow these steps:

Step 1: Ensure that the coefficient of the x^2 term is 1.
If the coefficient of x^2 is not 1, divide the entire equation by that coefficient (in this case, it's already 1, so no changes are needed).

x^2 + 9x + 6 = 0

Step 2: Move the constant term to the other side of the equation.
Subtract 6 from both sides to isolate the squared and linear terms on the left side:

x^2 + 9x = -6

Step 3: Take half of the coefficient of the x-term and square it.
The coefficient of the x-term is 9. Half of 9 is 4.5, and squaring it gives us 20.25.

Step 4: Add this value to both sides of the equation.
Add 20.25 to both sides of the equation to complete the square on the left side:

x^2 + 9x + 20.25 = -6 + 20.25

This simplifies to:

(x + 4.5)^2 = 14.25

Step 5: Solve for x by taking the square root of both sides.
Taking the square root of both sides will cancel out the square term on the left side:

x + 4.5 = ±√(14.25)

Step 6: Solve for x.
Subtract 4.5 from both sides to isolate x:

x = -4.5 ± √(14.25)

This gives us two possible solutions for x:

x = -4.5 + √(14.25)
x = -4.5 - √(14.25)

These are the solutions obtained by completing the square.