Question

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

$x^2+22x$

Short answer

The required binomial square is${\left(x+11\right)}^2$.

Step-by-step solution

Step 1. Given information.

The given quadratic equation is:

$x^2+22x$

Step 2. Complete the square.

$x^2+22x$

The coefficient of x is 22.

Now find ${\left(\frac{1}{2}b\right)}^2$,

$$\begin{gathered} {\left(\frac{1}{2}b\right)}^2={\left(\frac{1}{2}·22\right)}^2 \\ ={\left(11\right)}^2 \\ =121 \end{gathered}$$

Now add 121 to the binomial to complete the square,

$x^2+22+121$

Rewrite as a binomial square,

${\left(x+11\right)}^2$