we have
\(f(x)=x^{2}-2x-3\)
Find the roots
Equate the function to zero
\(x^{2}-2x-3=0\)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
\(x^{2}-2x=3\)
Complete the square. Remember to balance the equation by adding the same constants to each side.
\(x^{2}-2x+1=3+1\)
\(x^{2}-2x+1=4\)
Rewrite as perfect squares
\((x-1)^{2}=4\)
Square root both sides
\((x-1)=(+/-)2\)
\(x=1(+/-)2\)
\(x=1+2=3\)
\(x=1-2=-1\)
therefore
the answer is
\(x=3\)
