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: 19

Answer

$x=\pm2\sqrt{6}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 3x^2-72=0 ,$ use the properties of equality and express the equation in the form $x^2=c.$ Then take the square root of both sides (Square Root Property) and simplify the resulting radical. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} 3x^2=72 \\\\ x^2=\dfrac{72}{3} \\\\ x^2=24 .\end{array} Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} x=\pm\sqrt{24} .\end{array} Writing the radicand as an expression that contains a factor that is a perfect power of the index and then extracting the root of that factor result to \begin{array}{l}\require{cancel} x=\pm\sqrt{4\cdot6} \\\\ x=\pm\sqrt{(2)^2\cdot6} \\\\ x=\pm2\sqrt{6} .\end{array}
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.