Question

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 \( 9 \)**.