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grace14 · Mar 28, 2009, 04:40 PM

I do not know how to do this problem and would really appreciate anyone who might explain it to me.
x(2x-1)=45 it's a quadratic equation.. trying to find the diminsions of a shape.
Grace

galactus · Mar 28, 2009, 04:48 PM

Expand it out and subtract 45 from both sides.

$2x^{2}-x-45=0$

It factors, so let's do that.

What two numbers when multiplied equal -90 and when added equal -1?

It is -90 because when we multiply the coefficient of x^2, 2, and the constant -45 we get -90. And the coefficient of x is -1.

Let's see... what could they be?

How about -10 and 9.

$2x^{2}-10x+9x-45$

Group:

$(2x^{2}-10x)+(9x-45)$

Factor out something common from each group:

$2x(x-5)+9(x-5)$

See? What's in the parentheses is the same. That is imperative or it won't work.

$(2x+9)(x-5)=0$

There ya' go. See how to do them now?

Solving for x: 2x+9=0, x=-9/2

x-5=0, x=5

The solutions are x=-9/2 and 5.

It crosses the x-axis at -9/2 and 5.

If you have to find the vertex, use $x=\frac{-b}{2a}=\frac{-(-1)}{2(2)}=\frac{1}{2}$

Plug that back into the original quadratic to find the corresponding y coordinate.

But what do you mean 'the dimensions of a shape'?

It's a parabola if you graph it.

grace14 · Mar 28, 2009, 04:51 PM

Thanks! What I meant by shape was, the problem asked me to find the dimensions of a shape, and I figured out the formula for it, I just didn't know how to slove the formula.

galactus · Mar 28, 2009, 04:52 PM

Oh, OK. I hope that helped. You could also just use the quadratic formula. That may be easier, but I like to factor if possible.

grace14 · Mar 28, 2009, 04:54 PM

Yes it really did help. Thanks so much!