Answer
a) $x=5$ or $x=-1$
b) $x=5$ or $x=-1$
c) $x=5$ or $x=-1$
The three methods give the same answers.
Work Step by Step
a) $x^2-4x-5=0\\(x-5)(x+1)=0$
Thus, $x=5$ or $x=-1$.
b) $x^2-4x-5=(x-2)^2-2^2-5=0\\(x-2)^2=9\\x-2=\pm3\\x=2\pm3$
Thus, $x=5$ or $x=-1$.
c) $x=\frac{4\pm\sqrt{(-4)^2-4(1)(-5)}}{2(1)}=\frac{4\pm\sqrt{36}}{2}=2\pm\sqrt{9}=2\pm3$
$x=5$ or $x=-1$.
