# My Son

• Feb 2nd 2010, 12:45 PM
divorce3
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
• Feb 2nd 2010, 01:05 PM
Quote:

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

$x^2+2x=48$

$x(x+2)=48$

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 $x^2+2x-48=0$

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

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

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

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,
• Feb 2nd 2010, 01:17 PM
pickslides
Quote:

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

Well you can, but it is not advised.

$x^2 + 2x = y$

$y = x^2 + 2x$

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

$x^2 + 2x = y$

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

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