Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

9.8.4 Practice

Algebra 19.8.4 Practice

Search for key terms or text.

Complete the following questions to practice the skills you have learned in this lesson.

  1. The quadratic equation x 2 + 7 x + 10 = 0 is in the form of a x 2 + b x + c = 0 .
  1. What is the value of a ?
  1. What is the value of b ?
  1. What is the value of c ?

Examine the solution method that has been started below and use it to answer parts d and e.

Original equation
x 2 + 7 x + 10 = 0

Step 1 - Subtract 10 from each side.
x 2 + 7 x = 10

Step 2 - Multiply each side by 4.
4 x 2 + 4 ( 7 x ) = 4 ( 10 )

Step 3 - Rewrite 4 x 2 as ( 2 x ) 2 and 4 ( 7 x ) as 2 ( 7 ) 2 x .
( 2 x ) 2 + 2 ( 7 ) ( 2 x ) + _ _ _ _ 2 = _ _ _ _ 2 4 ( 10 )

Step 4 - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
( 2 x + _ _ _ _ ) 2 = _ _ _ _ 2 4 ( 10 )

Step 5 - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
2 x + _ _ _ _ = ± _ _ _ _ 2 4 ( 10 )

Step 6 - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
2 x = _ _ _ _ ± _ _ _ _ 2 4 ( 10 )

Step 7 - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
x = _ _ _ _

  1. In Step 2, what might be a good reason for multiplying each side of the equation by 4?
  1. Multiplying by 4 makes the coefficient of the squared term a perfect square, which makes it easier to complete the square.
  2. Multiplying by 4 makes the coefficient of the b term a perfect square, which makes it easier to complete the square.
  3. If the value of c is positive and you multiply by 4, it will be easier to divide the b term by 3 before you square it.
  4. You must always multiply both sides by 4 when completing the square.
  1. Complete the unfinished steps, then select two solutions.
  1. -10
  2. -5
  3. -2
  4. -4
  1. Substitute the values of a , b , and c into the quadratic formula, x = b ± b 2 4 a c 2 a , but do not evaluate any of the expressions. Explain how this expression is related to solving x 2 + 7 x + 10 = 0 by completing the square.
  1. For this equation, the quadratic formula and completing the square are not the same and therefore not related.
  2. They are related because neither one can have a negative c value.
  3. Rather than evaluating at each step, the calculation is done all at once, at the end.
  4. In both forms of solving the equation, you need to list the values of a , b , and c to determine the solutions.
  1. Consider the standard form of the equation x 2 39 = 0 .
  1. What is the value of a ?
  1. What is the value of b ?
  1. What is the value of c ?
  1. Can you use the quadratic formula to solve this equation?
  1. No
  2. Yes
  1. Can you solve this equation using square roots?
  1. No, this equation can only be solved by the quadratic formula.
  2. Yes, the solutions are ± 39 .
  3. No, there is no solution.
  4. Yes, the solutions are ± 39 .
  1. Clare is deriving the quadratic formula by solving a x 2 + b x + c = 0 by completing the square.

She arrived at this equation: ( 2 a x + b ) 2 = b 2 4 a c .

Choose the best description of what she needs to do to finish solving for x .

  1. Find the square roots of each side. Divide each side by 2. Subtract b from each side.
  2. Divide each side by 2. Subtract b from each side. Then find the square roots of each side.
  3. Find the square roots of each side. Subtract b from each side. Then divide each side by 2 a .
  4. Subtract b 2 from each side. Find the square roots of each side. Then divide each side by 2.
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.