• May 24th 2010, 12:53 PM
fetuslasvegas
Can somebody help break this problem down for me using the quadratic formula? Thanks!

x^2+2x-2=0

I know the answer is x=-1 plusminus square root 3 (don't know how to write that on here)
• May 24th 2010, 01:00 PM
e^(i*pi)
Quote:

Originally Posted by fetuslasvegas
Can somebody help break this problem down for me using the quadratic formula? Thanks!

x^2+2x-2=0

I know the answer is x=-1 plusminus square root 3 (don't know how to write that on here)

For $\displaystyle ax^2+bx+c = 0$ then $\displaystyle x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

If you compare your equation to $\displaystyle ax^2+bx+c=0$ then you'll see that $\displaystyle a=1$, $\displaystyle b=2$ and $\displaystyle c=-2$. The place most people split up is a sign error when calculating $\displaystyle b^2-4ac$
• May 24th 2010, 01:14 PM
fetuslasvegas
Quote:

Originally Posted by e^(i*pi)
For $\displaystyle ax^2+bx+c = 0$ then $\displaystyle x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

If you compare your equation to $\displaystyle ax^2+bx+c=0$ then you'll see that $\displaystyle a=1$, $\displaystyle b=2$ and $\displaystyle c=-2$. The place most people split up is a sign error when calculating $\displaystyle b^2-4ac$

So I know this is sort of what it would look like when I go through the process, Where do I go from there to get the answer?

$\displaystyle x = \frac{-2 \pm \sqrt{2^2-4*1*-2}}{2*1}$
• May 24th 2010, 01:20 PM
harish21
Quote:

Originally Posted by fetuslasvegas
So I know this is sort of what it would look like when I go through the process, Where do I go from there to get the answer?

$\displaystyle x = \frac{-2 \pm \sqrt{2^2-4*1*-2}}{2*1}$

$\displaystyle x = \frac{-2 \pm \sqrt{4+8}}{2}$

$\displaystyle x = \frac{-2 \pm \sqrt{12}}{2}$

$\displaystyle x = \frac{-2 \pm 2\sqrt{3}}{2}$

so,

$\displaystyle x = \frac{-2 + 2\sqrt{3}}{2} = {\sqrt{3} -1}$
OR
$\displaystyle x = \frac{-2 - 2\sqrt{3}}{2}= {-\sqrt{3} -1}$

Both values of x satisfy your equation
• May 24th 2010, 01:26 PM
fetuslasvegas
Quote:

Originally Posted by harish21
$\displaystyle x = \frac{-2 \pm \sqrt{4+8}}{2}$

$\displaystyle x = \frac{-2 \pm \sqrt{12}}{2}$

$\displaystyle x = \frac{-2 \pm 2\sqrt{3}}{2}$

so,

$\displaystyle x = \frac{-2 + 2\sqrt{3}}{2} = {\sqrt{3} -1}$
OR
$\displaystyle x = \frac{-2 - 2\sqrt{3}}{2}= {-\sqrt{3} -1}$

Both values of x satisfy your equation

Ok I get mostly everything except where the -1 comes in?

The way I see the answer is $\displaystyle x = \frac{\sqrt{3}}{2}$
• May 24th 2010, 01:35 PM
harish21
Quote:

Originally Posted by fetuslasvegas
Ok I get mostly everything except where the -1 comes in?

The way I see the answer is $\displaystyle x = \frac{\sqrt{3}}{2}$

$\displaystyle x = \frac{-2 + 2\sqrt{3}}{2} = \frac{2(-1 + \sqrt{3})}{2}= -1 + \sqrt{3}= \sqrt{3}-1$

same for the second part
• May 24th 2010, 01:45 PM
fetuslasvegas
Quote:

Originally Posted by harish21
$\displaystyle x = \frac{-2 + 2\sqrt{3}}{2} = \frac{2(-1 + \sqrt{3})}{2}= -1 + \sqrt{3}= \sqrt{3}-1$

same for the second part

I see how it makes sense, I just am not getting where this -1 is coming from or what you are doing to get the -1. Is it coming from moving the negative sign from the first two which for some reason subtracts from the second 2?
• May 24th 2010, 01:54 PM
pickslides
Quote:

Originally Posted by fetuslasvegas
I see how it makes sense, I just am not getting where this -1 is coming from or what you are doing to get the -1. Is it coming from moving the negative sign from the first two which for some reason subtracts from the second 2?

$\displaystyle -2+2\sqrt{3} = 2\times -1+2\times \sqrt{3}$

Now 2 is common to both terms so it can be factored out giving

$\displaystyle 2\times -1+2\times \sqrt{3} = 2(-1+\sqrt{3})$

• May 24th 2010, 02:12 PM
fetuslasvegas
Quote:

Originally Posted by pickslides
$\displaystyle -2+2\sqrt{3} = 2\times -1+2\times \sqrt{3}$

Now 2 is common to both terms so it can be factored out giving

$\displaystyle 2\times -1+2\times \sqrt{3} = 2(-1+\sqrt{3})$