My Son

**divorce3** · February 2nd 2010, 12:45 PM

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

**Archie Meade** · February 2nd 2010, 01:05 PM

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,
square it and add 2x and call the answer y.

**pickslides** · February 2nd 2010, 01:17 PM

Originally Posted by Archie Meade

For the first one, you need more information, because you can take any x,
square it and add 2x and call the answer y.

Well you can, but it is not advised.

You already have the answer for y

$x^2 + 2x = y$

$y = x^2 + 2x$

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

$x^2 + 2x = y$

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

by the quadratic formula

$x=\frac{-2\pm\sqrt{2^2-4(1)\times (-y)}}{2}$

This can be simplified to

$x = -1\pm\sqrt{1+y}$

**HallsofIvy** · February 3rd 2010, 04:33 AM

How is that different from just saying $y= x^2+ 2x$ for any value of x?

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