Question 892179
First solve {{{x^2=64}}}
{{{x^2-64=0}}}
{{{(x-8)(x+8)=0}}}
Two solutions:
{{{x-8=0}}}
{{{x=8}}}
and
{{{x+8=0}}}
{{{x=-8}}}
Now break up the number line using these two critical numbers and test the inequality.
{{{x<-8}}}
{{{-8<x<8}}}
{{{x>8}}}
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{{{x<-8}}}
{{{x=-10}}}
{{{(-10)^2-64<0}}}
{{{100-64< 0}}}
{{{36<0}}}
False, not in the solution region.
.
.

{{{x=0}}}
{{{0^2-64<0}}}
{{{-64<0}}}
True, in the solution region.
.
.
{{{x>8}}}
{{{x=10}}}
{{{(10)^2-64<0}}}
{{{100-64< 0}}}
{{{36<0}}}
False, not in the solution region.
.
.
{{{highlight(-8<x<8)}}}