Question

PLEASE HELP!! i keep figuring this out but im kind of confused
1. Calculate the number that you need to add to each side of the equation w^2 - 3w = 350 to create a perfect square trinomial.

2. Factor the trinomial.

3. Now that you've factored the equation, find the square root of each side and solve for w.

Answer 1

It's completing the square, is it not?

Answer 2

For completing the square problems, always start out with generic square and multiplying it:\[
(x+s)^2=x^2+2sx+s^2
\]The term we will add to both sides is \(s^2\).
Now if we have an equation: \[
x^2+bx+c
\]We can say \(b=2s\) and thus \(s^2 = (b/2)^2\). We add \((b/2)^2\) to both sides.

Answer 3

You've provided an equation where \(b=-3\), so we need to add \((-3/2)^2=9/4\) to both sides.

Answer 4

Well, you can just memorize the \((b/2)^2\) term, but multiplying a generic square allows you to derive it rather quickly.

Answer 5

@wio i got this
w^2-3w=350
w^2-3w +(-3/2)^2=350
w^2-3w +(9/4) =350 +(9/4)

Answer 6

Now remember that \(s=-3/2\), so that means:\[
w^2-3w+(9/4) = (w-3/2)^2
\]

Answer 7

This comes from our equation \[
x^2+2s+s^2=(x+s)^2
\]but we use \(w\) instead of \(x\).

Answer 8

If we take the square root of both sides, we get: \[
|w-3/2| = \sqrt{350+9/4}
\]Which means \[
w = -3/2\pm \sqrt{350+9/4}
\]You should simplify the square root though.

Answer 9

dont u have to square the -3/2

Answer 10

No, why would you need to square it?

Answer 11

@wio i got this
w^2 - 3/2 = square root of 352.25

Answer 12

What should i do nxt??