Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Exercise Set: 40

Answer

$x=(\frac{-3+\sqrt 17}{2}, \frac{-3-\sqrt 17}{2})$

Work Step by Step

Step-1 : Add $2$ from both sides of the equation $x^2+3x=2$ Step -2 : Add the square of half of the co-efficient of $x$ to both sides. Co-efficient of $x =3$ Half of $3 = \frac{1}{2}×3=\frac{3}{2}$ Square of $\frac{3}{2}$ is $\frac{3}{2}×\frac{3}{2}=\frac{9}{4}$ The equation becomes $x^2+3x+\frac{9}{4}=2+\frac{9}{4}$ Step-3 Factor the trinomial and simplify the right hand side. $(x+\frac{3}{2})^2=\frac{8+9}{4}$ $(x+\frac{3}{2})^2=\frac{17}{4}$ Step-4 Use the square root property and solve for $x$ $(x+\frac{3}{2})=±\sqrt\frac{17}{4} $ Step-5 Subtract \frac{3}{2} on both the sides $x=-\frac{3}{2}±\sqrt \frac{17}{4}$ Step-6 Simplify the right hand side $x=-\frac{3}{2}±\frac{\sqrt 17}{2}$ $x=\frac{-3±\sqrt 17}{2}$ Therefore the solution set is $(\frac{-3+\sqrt 17}{2}, \frac{-3-\sqrt 17}{2})$
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