Question 91222
{{{x^2+18x}}} Start with the given expression


Take half of the x coefficient 18 to get 9 (ie {{{18/2=9}}})

Now square 9 to get 81 (ie {{{9^2=81}}})


Now add 81 to the expression {{{x^2+18x}}}


{{{x^2+18x+81}}}


So {{{x^2+18x+81}}} is now a perfect square


Check:


Notice if we factor {{{x^2+18x+81}}}, we get {{{(x+9)^2}}}. So this verifies that {{{x^2+18x+81}}} is a perfect square.