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## #1 2006-09-22 07:17:47

longman619
Member
Registered: 2006-09-14
Posts: 3

### Equations Help

Hey, I'm having trouble with a few of these.

1. x^2 - 6x + 3 = 0

2. x^2 + 5x + 1 = 0

3. 2x^2 - 50 = 0

4. x = 3/x + 7

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## #2 2006-09-22 08:12:17

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Equations Help

Those are quadratic equations. It looks like they won't factorise, so you need to either complete the square of use the quadratic formula. The quadratic formula is quicker, so I recommend that way.

If ax² + bx + c = 0, then x = (-b ± √(b² - 4ac))/(2a).
(Look at the post below for a clearer version of this. My LaTeX is terrible.)

So in your first question, a = 1, b = -6 and c = 3, so x = (6 ±√(6² - 4*1*3))/2*1

This works out to be 3 ± √6.

Your other three questions can be worked out in exactly the same way. Number 4 needs a bit of rearranging first though.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2006-09-22 08:15:36

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Equations Help

to rewrite in latex

for 4)

multiply by x

Last edited by luca-deltodesco (2006-09-22 08:16:46)

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #4 2006-09-24 01:07:50

longman619
Member
Registered: 2006-09-14
Posts: 3

### Re: Equations Help

I get x=9.25 or x= 4.71 for number 4 - can someone check this

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## #5 2006-09-24 02:45:00

Dross
Member
Registered: 2006-08-24
Posts: 325

### Re: Equations Help

longman619 wrote:

I get x=9.25 or x= 4.71 for number 4 - can someone check this

Ah, but the beauty of these questions is that you can check them yourself! Simply plug one of your values for x into the equation, and see if it works.

So if you wanted to check your solution of x = 9.25, you'd just see if:

was true or not. Unfortunately, I don't think your answer was correct - I get: