Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.4 Quadratic Equations - 1.4 Exercises - Page 121: 42


$\color{blue}{\left\{5-\sqrt7, 5+\sqrt7\right\}}$.

Work Step by Step

Add $-18$ to both sides: $x^2-10x=-18$ Add the square of one-half of the coefficient of $x$, which is $(\frac{-10}{2})^2=(-5)^2=25$, to obtain: $x^2-10x+25=-18+25 \\(x-5)^2=7$ Take the square root of both sides to obtain: $\sqrt{(x-5)^2}=\pm \sqrt{7} \\x-5 = \pm \sqrt7$ Add $5$ to both sides: $x=5 \pm \sqrt7$ Thus, the solution set is: $\color{blue}{\left\{5-\sqrt7, 5+\sqrt7\right\}}$.
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