Originally Posted by
skeeter the method is called completing the square.
$\displaystyle 2x^2 - 10x - 7$ This is the original equation
$\displaystyle 2(x^2 - 5x) - 7$ Here he factored a 2 out since you must have a coefficient of 1 in front of your squared term to complete the square
$\displaystyle 2\left(x^2 - 5x + \frac{25}{4}\right) - 7 - \frac{25}{2}$ the 25/4 comes from taking the coefficient of the linear term divided by 2 and then squaring that value...so (5/2)^2=(25/4)...you then add (25/4) to what you have in parenthesis and subtract the same ammount that you added times the coefficient of your quadratic equation which in this case is two so subtract (25/2)...doing this makes it so that you are really adding zero to the equation but making it easy to factor
$\displaystyle 2\left(x - \frac{5}{2}\right)^2 - \frac{39}{2}$then you just factor the quadratic