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: 61

Answer

$z=1$ and $z=-4$

Work Step by Step

$z^{2}+3z-4=0$ Take the $4$ to the right side of the equation: $z^{2}+3z=4$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this case, $b=3$ $z^{2}+3z+\Big(\dfrac{3}{2}\Big)^{2}=4+\Big(\dfrac{3}{2}\Big)^{2}$ $z^{2}+3z+\dfrac{9}{4}=\dfrac{25}{4}$ Factor the expression on the left side of the equation, which is a perfect square trinomial: $\Big(z+\dfrac{3}{2}\Big)^{2}=\dfrac{25}{4}$ Take the square root of both sides of the equation: $\sqrt{\Big(z+\dfrac{3}{2}\Big)^{2}}=\sqrt{\dfrac{25}{4}}$ $z+\dfrac{3}{2}=\pm\dfrac{5}{2}$ Solve for $z$: $z=\dfrac{-3\pm5}{2}$ The two solutions are: $z=\dfrac{-3+5}{2}=1$ $z=\dfrac{-3-5}{2}=-4$
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