Question 1090512
Graphically,
.
.
.
*[illustration T8.JPG].
.
.
.
Factoring,
{{{f(x)=-3x^2+27x-42}}}
{{{f(x)=-3(x^2-9x+14)}}}
{{{f(x)=-3(x-2)(x-7)}}}
.
.
.
Completing the square,
{{{f(x)=-3(x^2-9x)-42}}}
{{{f(x)=-3(x^2-9x+(9/2)^2)-42+3(9/2)^2}}}
{{{f(x)=-3(x-9/2)^2-42+243/4}}}
{{{f(x)=-3(x-9/2)^2-168/4+243/4}}}
{{{f(x)=-3(x-9/2)^2+75/4}}}
So,
{{{-3(x-9/2)^2+75/4=0}}}
{{{3(x-9/2)^2=75/4}}}
{{{(x-9/2)^2=25/4}}}
{{{x-9/2=0 +- 5/2}}}
{{{x=9/2+-5/2}}}
.
.
{{{x=14/2=7}}}
{{{x=4/2=2}}}