## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises: 23

#### Answer

$x=\pm4\sqrt{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $3x^2-10=86 ,$ 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=86+10 \\\\ 3x^2=96 \\\\ x^2=\dfrac{96}{3} \\\\ x^2=32 .\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{32} .\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{16\cdot2} \\\\ x=\pm\sqrt{(4)^2\cdot2} \\\\ x=\pm4\sqrt{2} .\end{array}

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.