If using the method of completing the square to solve the quadratic equation x, squared, minus, 6, x, plus, 6, equals, 0x 2 −6x+6=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square for the quadratic equation \( x^2 - 6x + 6 = 0 \), we need to focus on the quadratic and linear terms, \( x^2 - 6x \).

1. Identify the coefficient of the \( x \) term: The coefficient of \( x \) is \(-6\).

2. Take half of this coefficient and square it:

   • Half of \(-6\) is \(-3\).
   • Squaring \(-3\) gives \((-3)^2 = 9\).

3. Add this square (9) to both sides of the equation to keep it balanced.

Thus, the number that needs to be added to complete the square is \( 9 \).

The equation can be rewritten as follows after adding 9 to both sides:

\[ x^2 - 6x + 9 = 3 \]

Now, \( x^2 - 6x + 9 \) can be factored as \( (x - 3)^2 \).

In summary, the number that would have to be added to complete the square is \( 9 \).