1. ## My Son

It has been a great many years since I did any algebra, now my son hits me with this:-

x squared + 2x = y find x and y

x squared + 2x = 48 find x

2. Originally Posted by divorce3
It has been a great many years since I did any algebra, now my son hits me with this:-

x squared + 2x = y find x and y

x squared + 2x = 48 find x
For the second one, you could write

$\displaystyle x^2+2x=48$

$\displaystyle x(x+2)=48$

The factors of 48 that differ by 2 are 6 and 8, so x=6
or -6 and -8 so x=-8 as that is 2 less than -6.

Or $\displaystyle x^2+2x-48=0$

$\displaystyle (x-a)(x-b)=x(x-b)-a(x-b)=x^2-bx-ax+ab=x^2-(a+b)x+ab$

We are looking for the factors of -48 that add to give 2,
these are -6 and 8, since

$\displaystyle (x-6)(x+8)=0$

Two values multiplied give zero means x-6=0 or x+8=0,
so x=6 or -8.

For the first one, you need more information, because you can take any x,

3. Originally Posted by Archie Meade
For the first one, you need more information, because you can take any x,
Well you can, but it is not advised.

$\displaystyle x^2 + 2x = y$

$\displaystyle y = x^2 + 2x$

To solve for $\displaystyle x$ in the first equation you can say

$\displaystyle x^2 + 2x = y$

$\displaystyle x^2 + 2x - y=0$

$\displaystyle x=\frac{-2\pm\sqrt{2^2-4(1)\times (-y)}}{2}$
$\displaystyle x = -1\pm\sqrt{1+y}$
4. How is that different from just saying $\displaystyle y= x^2+ 2x$ for any value of x?