Chapter 3.3, Problem 3AYU

To complete the square of $x^2-5x$, you add the number ______. (p. A49)

To determine

To fill: The blank of the given statement “To complete the square of $x^2-5x$ you add the number _______”.

Answer to Problem 3AYU

“To complete the square of $x^2-5x$ you add the number $\frac{25}{4}.$”

Explanation:

Given:

The given statement is

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

Consider the general equation $x^2+mx.$

In order to complete the square of the above equation, we have to add the square of half of $m.$

Therefore, we have to add ${\left(\frac{m}{2}\right)}^2.$

Here, the given equation is $x^2-5x.$

Thus we have $m=-5.$

Now, in order to complete the square of the give equation, we have to add ${\left(\frac{-5}{2}\right)}^2=\frac{25}{4}.$

Explanation of Solution

Given:

The given statement is

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

Consider the general equation $x^2+mx.$

In order to complete the square of the above equation, we have to add the square of half of $m.$

Therefore, we have to add ${\left(\frac{m}{2}\right)}^2.$

Here, the given equation is $x^2-5x.$

Thus we have $m=-5.$

Now, in order to complete the square of the give equation, we have to add ${\left(\frac{-5}{2}\right)}^2=\frac{25}{4}.$