Chapter 10.4, Problem 2AYU

To determine

To find: The term that needs to be added to complete the square of $x²+5x$.

Answer to Problem 2AYU

Solution:

$25/4$

Explanation of Solution

Given:

$x²+5x$

Formula used:

$x^2+bx+{\left(\frac{b}{2}\right)}^2={\left(x+\frac{b}{2}\right)}^2$

Calculation:

Consider $x^2+5x$.

From the formula, we see that $b=5$.

To make it square we add, ${\left(\frac{b}{2}\right)}^2={\left(\frac{5}{2}\right)}^2=25/4$.

Hence, we add $\frac{25}{4}$ to complete the square $x²+5x$ so that,

$x^2+5x+\frac{25}{4}={\left(x+\frac{5}{2}\right)}^2$