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

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

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) (Show Source): You can put this solution on YOUR website!

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:

Find 1/2 of 10 (which would be 5)
Square the 5 (which would be 25)
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:

Now that the square has been completed we can solve the equation. Finding the square root of each side:

which, remembering the positive and negative square roots, gives us:
w + 5 = +

Adding -5 to each side we get:
w = -5 +

which is short for:
w = -5 + 1/2 or w = -5 - 1/2
which simplify to:
or
RELATED QUESTIONS
7+w=-4-10w (answered by Fombitz)

I know this is not difficult...but, not quite sure...not judging by the multiple choice... (answered by nerdybill)

Solve the equation by the zero-factor property. w^2-10w+21=0 The solution set... (answered by Alan3354)

(2w^5+16w^4-10w^3-4w^2)\w^2 (answered by mattizzyo)

-2(w-7)+10w=34 (answered by nerdybill)

solve... (answered by jim_thompson5910)

how do i solve -5(10w+1)=25 (answered by Alan3354)

solve the polynomial... (answered by scott8148)