Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Review Exercises - Page 657: 15

Answer

$\{1-3i\sqrt 2,1+3i\sqrt 2\}$

Work Step by Step

We have to solve the equation: $$x^2-2x+19=0.$$ The equation is in the standard form. To solve the equation $ax^2+bx+c=0$ we will use the quadratic formula: $$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$ Identify $a$, $b$, $c$: $$\begin{align*} a&=1\\ b&=-2\\ c&=19. \end{align*}$$ We solve the given equation by substituting the values of $a$, $b$, $c$ in the quadratic formula: $$\begin{align*} x&=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(19)}}{2(1)}\\ &=\dfrac{2\pm\sqrt{-72}}{2}\\ &=\dfrac{2\pm 6\sqrt 2i}{2}\\ &=1\pm3i\sqrt 2. \end{align*}$$ The solution set of the equation is: $$\{1-3i\sqrt 2,1+3i\sqrt 2\}.$$
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