Question 650909
You realize that
{{{x^2-6x+9=(x-3)^2}}} and re-write the equation as
{{{x-3)^2=100}}}
Since {{{10^2=100}}} and {{{(-10)^2=100}}} ,
that leads you to the two solutions.
Either {{{x-3=10}}} --> {{{x=10+3}}} --> {{{highlight(x=13)}}}
or {{{x-3=-10}}} --> {{{x=-10+3}}} --> {{{highlight(x=-7)}}}
 
Not all equations will be that close to the solution.
If they had given you
{{{x^2-6x-91=0}}} or the equivalent equation {{{x^2-6x=91}}}
you would have to realize that {{{x^2-6x}}} is almost {{{x^2-6x+9=(x-3)^2}}}
Then, adding 9 to both sides of the equal sign in {{{x^2-6x=91}}} ,
you would get to {{{x^2-6x+9=100}}}
The adding of a number to get a perfect square is what math teachers call "completing the square."