Question

If using the method of completing the square to solve the quadratic equation x, squared, minus, 2, x, minus, 1, equals, 0x
2
−2x−1=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square for the quadratic equation \( x^2 - 2x - 1 = 0 \), we first focus on the expression \( x^2 - 2x \).

To complete the square, we follow these steps:

1. Take the coefficient of \( x \), which is \(-2\).
2. Divide it by 2: \(-2 / 2 = -1\).
3. Square the result: \((-1)^2 = 1\).

Now, to complete the square, we need to add \(1\) to the expression. So, you would add \(1\) to both sides of the equation:

\[
x^2 - 2x + 1 = 1 - 1
\]

This gives us:

\[
(x - 1)^2 = 0
\]

Thus, to complete the square, you would add \(1\).