Question 292771
 w^2-14w+24=0

1.) w^2 - 14w = -24

We need to add the same constant to both sides to get the left side to factor into (x-a)^2 

If we take half the coefficent on w (that is -14) and then square it we will have the constant we are looking for. -14/2 = -7. If we square -7 we get 49. So we will add 49 to both sides of 1.):

w^2 - 14w + 49 = -24 + 49
(w-7)^2 = 25

w-7 = sqrt(25) or w-7 = -sqrt(25)

w-7 = 5 or w-7 = -5

w = 12 or w = 2