Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 631: 36


$x=\left\{ 5-\sqrt{3},5+\sqrt{3} \right\}$

Work Step by Step

The left side of the given equation, $ x^2-10x+25=3 ,$ is a perfect square trinomial whose factored form is \begin{array}{l}\require{cancel} (x-5)^2=3 .\end{array} Taking the square root of both sides (the Square Root Property), the solutions to the given equation are \begin{array}{l}\require{cancel} x-5=\pm\sqrt{3} \\\\ x=5\pm\sqrt{3} .\end{array} Hence, $ x=\left\{ 5-\sqrt{3},5+\sqrt{3} \right\} .$
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