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