Answer
$[-5, 5]$
Work Step by Step
$2x^2-50 <= 0$
$(2x^2-50)/2 <= 0$
$x^2-25 <=0$
$(x-5)(x+5) <=0$
$x-5 <=0$
$x-5+5 <=0+5$
$x <=5$
$x+5 <=0$
$x+5-5 <=0-5$
$x <=-5$
Three regions to test: $(-∞, -5]$, $[-5, 5]$, $[5, ∞)$
Let $x=-10$, $x=0$, $x=10$
$x=-10$
$2x^2-50 <= 0$
$2(-10)^2-50 <= 0$
$2*100-50 <=0$
$200-50 <=0$
$150 <=0$ (false)
$x=0$
$2x^2-50 <= 0$
$2*0^2-50 <= 0$
$2*0-50 <= 0$
$-50 <=0$ (true)
$x=10$
$2x^2-50 <= 0$
$2(10)^2-50 <= 0$
$2*100-50 <=0$
$200-50 <=0$
$150 <=0$ (false)
