Completing the square

Question

How do you solve this problem by completing the square?

 

x^2+6x=9

Answer 1

As follow-up to the David's solution, the value to be added to both sides can be calculated by...

 

...looking at your original expression, identify the coefficient "B" of the "x" term.  Take one-half the "B" value, then square the result and can written as [½(B)]² or [B/2]².  This value is added to both sides of the equation.  So, with the above...

 

B=6..................from Ax²+Bx=C ----> x²+6x=9, original equation

1/2(6)=6/2=3...take one-half of "B"

3²=9................square the value found in the previous step

 

This is the exact value David added to each side of the equation in his solution.

 

Answer 2

"Completing the square" is a method of solving equations by changing part of an expression into a perfect square expression (thus, adding to both sides of an equation).
 
The expression here is:  x²+6x
This is part of the perfect square expression:    x²+6x+9 = (x+3)(x+3)     [verify this using F-O-I-L!]
 
So, add 9 to both sides of the given equation:
    x² + 6x + 9 = 9+9
    (x+3)² = 18
then take the square root of both sides:
    √(x+3)² = √18
       x+3 = ±3√2
     x = (-3 + 3√2)  or   x = (-3 - 3√2)