SOLUTION: {{{X^2-6x=16}}} I'm supposed to solve this by completing the square.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: {{{X^2-6x=16}}} I'm supposed to solve this by completing the square.      Log On


   

Question 19274: X%5E2-6x=16 I'm supposed to solve this by completing the square.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
right, fairly easy concept here. As follows:

x%5E2-6x=16 Just look at the left hand side: x%5E2-6x. We need to figure out which number to add/subtract such that we can then factorise it as x%2Ba%29%5E2 or %28x-a%29%5E2

so, x%2Ba%29%5E2 expanded would give x%5E2+%2B+2ax+%2B+a%5E2 and the negative version would have -2ax instead.

So, we have -6x which is the (-2ax) which means that a needs to be 3.

So, the a%5E2 term is 3%5E2 ---> 9

So, we have to add 9...to both sides remember, to keep the equation unaltered... x%5E2-6x%2B9+=+25
So, x%5E2+-+6x+%2B+9 can be written instantly as %28x-3%29%5E2 --> the negative version, since the x-term was negative.

and we have %28x-3%29%5E2+=+25
%28x-3%29+=+%2Bsqrt%2825%29 OR %28x-3%29+=+-sqrt%2825%29

--> x-3 = +5 OR x-3 = -5
--> x = 8 OR x = -2

jon.