Lost calculator...need help!! Quadratic Formula

[Leci03]

I have been trying to figure this out in my head, but it's giving me fits!!

6x[sup:179lz4j8]2[/sup:179lz4j8] - 3x - 18 = 0
x = [sup:179lz4j8]-(-3)+- square root of -(-3)^2 -4(6)(-18)[/sup:179lz4j8] /[sub:179lz4j8]2(6)[/sub:179lz4j8]
x = [sup:179lz4j8]3 +- square root of 9 - 432[/sup:179lz4j8]/[sub:179lz4j8]12[/sub:179lz4j8]
x = [sup:179lz4j8]3 +- square root of 423[/sup:179lz4j8]/ [sub:179lz4j8]12[/sub:179lz4j8]

I cannot figure out if I can simplify from there, I'm lost without my calculator, I would appreciate any help

 

[galactus]

What exactly are you doing?. I don't understand that little font.

Anyway, I would assume you are factoring?. I always preferred factoring over the formula if practical to do. This one factors nicely.

\(\displaystyle 6x^{2}-3x-18=0\)

Factor out a 3:

\(\displaystyle 3(2x^{2}-x-6)=0\)

Now, factor inside the parentheses:

What two numbers multiplied equal -12 and when added equal -1?. How about -4 and 3?.

\(\displaystyle 2x^{2}-4x+3x-6\)

Group:

\(\displaystyle (2x^{2}-4x)+(3x-6)=0\)

Factor:

\(\displaystyle 2x(x-2)+3(x-2)=0\)

\(\displaystyle 3(2x+3)(x-2)=0\)

Now, what values of x result in 0?. Those are your solutions.

See what to do now?. Try not being so calculator dependent. You never know when you may have to do it the old-fashioned way.

But, if you use the formula:

\(\displaystyle x=\frac{-(-3)\pm\sqrt{(-3)^{2}-4(6)(-18)}}{2(6)}\)

\(\displaystyle x=\frac{-(-3)\pm\sqrt{9+432}}{12}\)

\(\displaystyle x=\frac{-(-3)\pm\sqrt{441}}{12}\)

Now, finish up?. 441 is a perfect square.

 

[Leci03]

No, not factoring, I'm solving using the quadratic formula to find my x-coordinates. I appreciate the help, but factoring would have been easy. As far as using a calculator, I really just need to know if I can simplify the equation to smaller numbers still using whole numbers, however I'm not that math savvy without my hand held technology.

Okay, I got it, I made a sign error, now it makes a lot more sense. Thank you very much...

 

[Mrspi]

No, not factoring, I'm solving using the quadratic formula to find my x-coordinates. I appreciate the help, but factoring would have been easy. As far as using a calculator, I really just need to know if I can simplify the equation to smaller numbers still using whole numbers, however I'm not that math savvy without my hand held technology.

Okay, I got it, I made a sign error, now it makes a lot more sense. Thank you very much...

Your original equation was

6x[sup:1ljv5qzv]2[/sup:1ljv5qzv] - 3x - 18 = 0

No matter whether I am going to use the quadratic formula OR factoring, the first thing I'd look at is whether all terms of the equation can be divided by a common factor. If they can be, then DO that.

In your problem, 3 is a common factor of all the terms. Divide both sides of the equation by 3, and you'll get

2x[sup:1ljv5qzv]2[/sup:1ljv5qzv] - x - 6 = 0

Now, no matter which method you use to solve the equation, you've got smaller numbers and so have simplified the arithmetic.