Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises: 29

Answer

$x=\left\{ 4-\sqrt{3},4+\sqrt{3} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ (x-4)^2=3 ,$ take the square root of both sides (Square Root Property). Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} x-4=\pm\sqrt{3} .\end{array} Using the properties of equality to isolate the variable, the equation above is equivalent to \begin{array}{l}\require{cancel} x=4\pm\sqrt{3} .\end{array} The solutions are \begin{array}{l}\require{cancel} x=4-\sqrt{3} \\\\\text{OR}\\\\ x=4+\sqrt{3} .\end{array} Hence, $ x=\left\{ 4-\sqrt{3},4+\sqrt{3} \right\} .$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.