Chapter 9: Q.411. (page 982)

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$x^{2} + 22 x$

Short Answer

Expert verified

The solution is ${(x + 11)}^{2}$ .

Step by step solution

Step 1. Given information.

The given expression is $x^{2} + 22 x$ .

Step 2. Compare the given expression with x2+bx.

The given binomial expression is $x^{2} + 22 x$ .

On comparing with $x^{2} + b x$ , we have $b = 22$ .

So, the coefficient of $x$ is $22$ .

Step 3. Find the 12b2.

$\begin{array}{rcl} (\frac{1}{2} b^{2}) & = & {(\frac{1}{2} \cdot 22)}^{2} \\ = & {(11)}^{2} \\ = & 121 \end{array}$

Thus, the number to complete the square is $121$ .

Step 4. To complete the square, add 121in the given binomial expression.

$\begin{array}{rcl} x^{2} + 22 x + 121 & = & x^{2} + 2 \cdot x \cdot 11 + {(11)}^{2} \\ = & {(x + 11)}^{2} \end{array}$

Step 5. Simplified answer.

Hence, the required binomial square is $\begin{array}{rcl} {(x + 11)}^{2} \end{array}$ .

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In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$x^{2} + 22 x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare the given expression with x2+bx.

Step 3. Find the 12b2.

Step 4. To complete the square, add 121in the given binomial expression.

Step 5. Simplified answer.

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In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.x2+22x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare the given expression with x2+bx.

Step 3. Find the 12b2.

Step 4. To complete the square, add 121in the given binomial expression.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Decision Maths

Pure Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$x^{2} + 22 x$