Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

To complete the square of $x^2-5x$, you add the number _______.

Step-by-Step Solution

Answer

You need to add ${\left(\frac{-5}{2}\right)}^2$ or $\frac{25}{4}$ to complete the square.

Step 1. Given information.

The given expression is:

$x^2-5x$

Step 2. Determine the required value.

If the coefficient of $x^2$ is 1, then we complete the square by adding the square of one-half of the coefficient of $x$.

In the given expression, then the coefficient of $x^2$ is 1 and the coefficient of $x$ is $-5$.

The square of one-half of the coefficient of $x$ is:

${\left(\frac{-5}{2}\right)}^2=\frac{25}{4}$.

Step 3. Conclusion.

You need to add ${\left(\frac{-5}{2}\right)}^2$ or $\frac{25}{4}$ to complete the square.