Question

Which expression represents x^2-4x-5 in completed square form?

Answer 1

To express the quadratic \( x^2 - 4x - 5 \) in completed square form, we can follow these steps:

1. Start with the expression:
\[
x^2 - 4x - 5
\]

2. Focus on the quadratic and linear terms, \( x^2 - 4x \). To complete the square, we need to find a term that will allow us to rewrite it as a perfect square trinomial. We take half of the coefficient of \( x \) (which is \(-4\)), square it, and add and subtract that value:
- Half of \(-4\) is \(-2\).
- Squaring \(-2\) gives \(4\).

3. Add and subtract \(4\) inside the expression:
\[
x^2 - 4x + 4 - 4 - 5
\]

4. This simplifies to:
\[
(x - 2)^2 - 4 - 5
\]

5. Combine the constants \(-4\) and \(-5\):
\[
(x - 2)^2 - 9
\]

So, the completed square form of \( x^2 - 4x - 5 \) is:
\[
(x - 2)^2 - 9
\]