1. ## check my work on quadratic equations?

can someone check this for me?

3. No, both are wrong (first one in the answer, second one in the writing)

$\displaystyle \Rightarrow$ In the first one, you must write both answers :

$\displaystyle x = \frac{4}{\sqrt{5}}$ and $\displaystyle x = - \frac{4}{\sqrt{5}}$

$\displaystyle \Rightarrow$ The second one has the correct answer but is not correctly written. Here is an example of how it should be written :

$\displaystyle x^2 - 8x + 5 = 0$

$\displaystyle x^2 - 8x = -5$

$\displaystyle x^2 - 8x + 16 = 11$

$\displaystyle (x - 4)^2 = 11$

$\displaystyle x - 4 = \sqrt{11}$ or $\displaystyle x - 4 = - \sqrt{11}$

$\displaystyle x = \sqrt{11} + 4$ or $\displaystyle x = - \sqrt{11} + 4$

Thus $\displaystyle x = 4 \pm \sqrt{11}$

EDIT : talking about the first question in this post ...

4. $\displaystyle \frac{-4\pm 2\sqrt{10}}{2}= -2\pm \sqrt{10}$

5. You must show all your working

What if I didn't know what the quadratic formula was?

You're up to here:

$\displaystyle \frac {-4 \pm 2\sqrt10}{2}$

The next bit is wrong. You didn't factor 2 out of the -4.

6. The other question you posted is wrong too
I am not taking account of the quadratic equation written on it because I do not see the link with the following.

Here is how you do it :

$\displaystyle \frac{-4 \pm \sqrt{40}}{2} = \frac{-4 \pm \sqrt{4 \times 10}}{2}$

$\displaystyle = \frac{-4 \pm 2 \sqrt{10}}{2} = \frac{2(-2 \pm \sqrt{10})}{2}$ --> This is where you messed up : you did not factorize the $\displaystyle -4$.

$\displaystyle = -2 \pm \sqrt{10}$

Or, more conveniently :

$\displaystyle = 2 \mp \sqrt{10}$

7. can someone help me understand the factorization part?

8. Remember that $\displaystyle ab + ac = a(b + c)$. Here, you have :

$\displaystyle \frac{-4 \pm 2 \sqrt{10}}{2}$

This can be written :

$\displaystyle \frac{-2 \times 2 \pm 2 \sqrt{10}}{2}$

The common factor is two, so you factorize it over the addition. Since you are factorizing all the $\displaystyle 2$ (and not $\displaystyle -2$ !), they become $\displaystyle 1$ (some people prefer to remove them directly though) :

$\displaystyle \frac{2(-2 \times 1 \pm 1 \sqrt{10})}{2}$

Now you can cancel $\displaystyle 2$ out :

$\displaystyle -2 \times 1 \pm 1 \sqrt{10}$

Which is simplified to :

$\displaystyle -2 \pm \sqrt{10}$

Or, even more conveniently :

$\displaystyle 2 \mp \sqrt{10}$

9. still dont really folllow, sry

10. alright let's break it down.

We have

$\displaystyle -4\pm2\sqrt10$

if we had $\displaystyle 2x^2+4x$

we would factorise it by taking 2x out of the equation.

So we divide all terms by 2x:

$\displaystyle x+2$

So same as $\displaystyle -4\pm2\sqrt10$

we can take 2 out of the equation;

So divide everything by 2
you will get: $\displaystyle -2\pm\sqrt10$

I divided the -4 by 2 (which made -2) and 2 by 2 ( which made 1)

Is this more clear now?

11. i think i got it now, thx a bunch

12. Cool!