Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

To complete the square of $x^{2} - 3 x$ , add $______$ .

To complete the square of $x^{2} - 3 x$ , add role="math" localid="1646794628543" $\frac{9}{4}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Given Expression:

$x^{2} - 3 x$

We want to complete the square of the given expression with the missing terms.

Step 2. Solution

What it actually means to complete a square is to find a number $a$ that when added to the given expression enables the whole expression, including the added number, to be written as a square like in the following example:

$x^{2} - 3 x + a = {(x + b)}^{2}$

First expand the right side of the equality $x^{2} + b x + b^{2}$ .

Both sides of the equality are polynomials and even more, they are equal.

Therefore, coefficients in front of the same power of the variable $x$ must be the same.

For role="math" localid="1646795833717" $x^{2} : 1 = 1$ the quality obviously holds. Moving on to $x : - 3 = 2 b$

Therefore $b = - \frac{3}{2}$ . And finally $a = b^{2} = {(- \frac{3}{2})}^{2} = \frac{9}{4}$

Step 3. Conclusion:

Therefore, in order to complete the square add $\frac{9}{4}$ to the expression. You can check if the answer is correct by finding the square: $x^{2} - 3 x + \frac{9}{4} = {(x - \frac{3}{2})}^{2}$

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Precalculus Enhanced with Graphing Utilities

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Short Answer

To complete the square of $x^{2} - 3 x$ , add $______$ .

Step by Step Solution

Step 1. Given information.

Step 2. Solution

Step 3. Conclusion:

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To complete the square of $x^{2} - 3 x$ , add $______$ .