   SEARCH HOME Math Central Quandaries & Queries  Question from Julie, a student: x^2 - 6x = 16 Please, Help I am stuck on this math problem. I need to solve by completing the square. I need the steps of solving the problem and the answer, Please. Thank You in advance. Hi Julie,

I am going to illustrate using the equation x2 - 8x = -15. The instructions again are to solve for x by completing the square.

The key to solving this problem is recognizing a pattern. Examine the two expressions

(x + a)2 = x2 + 2ax + a2
(x - a)2 = x2 - 2ax + a2

In each case if you know the coefficient of x, + 2a or -2a, take half of it and square the result you get the constant term a2. (This observation is only true if the coefficient of x2 is 1.) Thus in my example where the coefficient of x is -8, half of it is -4 and (-4)2 = 16. Thus x2 - 8x + 16 is a square (x - 4)2. So here is how I proceed to solve the problem.

x2 - 8x = -15 add 16 to each side
x2 - 8x + 16 = -15 + 16
(x - 4)2 = 1
Thus x - 4 = ± 1 and therefore x = 4 ± 1.
Hence my answer is x = 3 or x = 5.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.