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