SOLUTION: Solve the equation by completing the square to obtain exact solutions. * w^2 + 10w + 25 = 1/4 * What I've tried : w^2+ 10w = 1/4 - 25

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the equation by completing the square to obtain exact solutions. * w^2 + 10w + 25 = 1/4 * What I've tried : w^2+ 10w = 1/4 - 25       Log On


   

Question 713829: Solve the equation by completing the square to obtain exact solutions.
* w^2 + 10w + 25 = 1/4
* What I've tried : w^2+ 10w = 1/4 - 25

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
w%5E2+%2B+10w+%2B+25+=+1%2F4
Subtracting 25 like you tried is the normal step at this point. So it is not an incorrect thing to do. But if you look ahead at the next steps you will see that it is unnecessary. The next steps would be:
  1. Find 1/2 of 10 (which would be 5)
  2. Square the 5 (which would be 25)
  3. Add the square to each side
These steps would just bring us back to where we started!? This means that the trinomial we started with is already a perfect square trinomial! We can just go directly from:
w%5E2+%2B+10w+%2B+25+=+1%2F4
to
%28w%2B5%29%5E2+=+1%2F4

Now that the square has been completed we can solve the equation. Finding the square root of each side:
sqrt%28%28w%2B5%29%5E2%29+=+sqrt%281%2F4%29
which, remembering the positive and negative square roots, gives us:
w + 5 = +1%2F2
Adding -5 to each side we get:
w = -5 +1%2F2
which is short for:
w = -5 + 1/2 or w = -5 - 1/2
which simplify to:
w+=+-4%261%2F2 or w+=+-5%261%2F2