Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 9 - Quadratic Functions and Equations - 9-8 Systems of Linear and Quadratic Equations - Lesson Check - Page 585: 5


$(-3, -3)$, $(-1.5,-1.5)$ Graphing is easier than completing the square.

Work Step by Step

Please see the graph. The orange line is $y=x$, and the green line is $y=2x^2+10x+9$. $2x^2+10x+9=x$ $2x^2+10x+9-x=x-x$ $2x^2+9x+9=0$ $(2x^2+9x+9)/2=0/2$ $x^2+4.5x+4.5=0$ $x^2+4.5x+(4.5/2)^2+4.5=0+(4.5/2)^2$ $x^2+4.5x+5.0625+4.5=5.0625$ $x^2+4.5x+5.0625+4.5-4.5=5.0625-4.5$ $(x+2.25)^2 = 9/16$ $\sqrt {(x+2.25)^2} = \sqrt {9/16}$ $x+2.25 = ±.75$ $x+2.25=.75$ $x+2.25-2.25=.75-2.25$ $x=-1.5$ $x+2.25=-.75$ $x+2.25-2.25=-.75-2.25$ $x = -3$
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