Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises: 60

Answer

$x=\dfrac{1}{2}$ $x=-\dfrac{7}{2}$

Work Step by Step

$x^{2}+3x-\dfrac{7}{4}=0$ Let's take the independent term to the right side of the equation: $x^{2}+3x=\dfrac{7}{4}$ Remember that, in order to complete the square, we need to add $(\dfrac{b}{2})^{2}$ to both sides of the equation. $b$ is always the coefficient of the first degree term. In this equation, $b=3$: $x^{2}+3x+(\dfrac{3}{2})^{2}=\dfrac{7}{4}+(\dfrac{3}{2})^{2}$ $x^{2}+3x+\dfrac{9}{4}=\dfrac{7}{4}+\dfrac{9}{4}$ $x^{2}+3x+\dfrac{9}{4}=\dfrac{16}{4}$ $x^{2}+3x+\dfrac{9}{4}=4$ We have a perfect square trinomial on the left side of the equation. We factor it and the equation becomes: $(x+\dfrac{3}{2})^{2}=4$ Take the square root of both terms: $\sqrt{(x+\dfrac{3}{2})^{2}}=\sqrt{4}$ $x+\dfrac{3}{2}=\pm2$ Solve for $x$: $x=-\dfrac{3}{2}\pm2$ The two solutions are: $x=-\dfrac{3}{2}+2=\dfrac{1}{2}$ and $x=-\dfrac{3}{2}-2=-\dfrac{7}{2}$
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