Question 24740
Begin by adding 5 to each side to get the variables alone on the left side:


{{{x^2 - 4x - 5 = 0}}}

{{{x^2 - 4x - 5 +5 = 0+ 5}}}


Prepare to add a number to each side of the equation that will make the left side of the equation a perfect square trinomial.  I like to add a blank space to each side to set this up.  Notice that in the process of completing the square, the coefficient of x^2 MUST BE 1.
{{{x^2 - 4x + _____ = 5 + ____}}}


Now, to make the perfect square trinomial, you need to take HALF of the coefficient of x, which is -4.  Half of -4 is -2, and then SQUARE the -2, which is +4.  Add PLUS 4 to each side of the equation:

{{{x^2 - 4x + 4 = 5 + 4}}}


{{{ (x-2)^2 = 9}}}


Next, take the square root of each side:
{{{x-2 = 0+-sqrt(9)}}}
{{{x-2 = 0+-3 }}}


Finally, add +2 to each side to isolate the x term:
{{{x = 2 +- 3}}}


This really means:
x= 2+3 = 5   OR 
x= 2-3 = -1


R^2 at SCC


P.S.  Of course, factoring WOULD have been a LOT easier!!!