Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Appendix A - A.4 - Quadratic Equations - Exercises - Page 556: 26


$x=-7~$ or $~x=3$

Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$ Then we can factor the trinomial as follows: $~x^2+bx+c = (x+r)~(x+s)$ We can rewrite the given equation: $x^2+4x=21$ $x^2+4x-21 = 0$ To factor the left side of the equation, we need to find two numbers $r$ and $s$ such that $r+s = 4$ and $r\times s = -21$. We can see that $(7)+(-3) = 4~$ and $(7)\times (-3) = -21$ We can solve the equation as follows: $x^2+4x=21$ $x^2+4x-21 = 0$ $(x+7)(x-3)=0$ $x=-7~$ or $~x=3$
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