Answer
$(-3, -3)$, $(-1.5,-1.5)$
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 $y=2x^2+10x+9$.
$2x^2+10x+9=x$
$2x^2+10x+9-x=x-x$
$2x^2+9x+9=0$
$(2x^2+9x+9)/2=0/2$
$x^2+4.5x+4.5=0$
$x^2+4.5x+(4.5/2)^2+4.5=0+(4.5/2)^2$
$x^2+4.5x+5.0625+4.5=5.0625$
$x^2+4.5x+5.0625+4.5-4.5=5.0625-4.5$
$(x+2.25)^2 = 9/16$
$\sqrt {(x+2.25)^2} = \sqrt {9/16}$
$x+2.25 = ±.75$
$x+2.25=.75$
$x+2.25-2.25=.75-2.25$
$x=-1.5$
$x+2.25=-.75$
$x+2.25-2.25=-.75-2.25$
$x = -3$
