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: 79

Answer

$y = \frac{8 \pm \sqrt{14}}{10}$

Work Step by Step

$Find$ $all$ $real$ $solutions$ $of$ $the$ $quadratic$ $equation:$ $10y^2-16y+5=0$ Use the Quadratic Equation Formula: $x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}$ $10y^2-16y+5$ $a = 10, b = -16, c = 5$ $y = \frac{-(-16) \pm \sqrt {(-16)^2- 4(10 \times 5)}}{2(10)}$ $y = \frac{16 \pm \sqrt {256- 200}}{20}$ $y = \frac{16 \pm \sqrt {56}}{20}$ $y = \frac{16 \pm \sqrt {56}}{20}$ [Note: $\sqrt{56} = \sqrt{4\times14} = \sqrt{4}\times\sqrt{14}$ = $2\sqrt{14}$] $y=\frac{16 \pm 2\sqrt {14}}{20}$ $y=\frac{2(8\pm\sqrt{14})}{20}$ $y = \frac{8 \pm \sqrt{14}}{10}$
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