# Isolating a variable (hard)

• Oct 12th 2009, 03:26 PM
Volcanicrain
Isolating a variable (hard)
How do I isolate x here?
48.99 = 36.34(1+x)^2 + ([(1+x)^2 - 1]/x)

I get to:
(1+x)^2 = (48.99x + 1)/(36.34x + 1)
But I can't simplify my equation further.

Also, x > 0. I know x = 0.1355 but I can't get to it algebraically.
• Oct 12th 2009, 03:46 PM
Raoh
$\frac{(1+x)^{2}(36.34x+1)-(48.99x+1)}{36.34x+1}=0$ $\Leftrightarrow 36.34 x^3+73.68 x^2-10.65 x=0$ solve for $x$ ,you'll get $x=0.13549$ for $x> 0$
• Oct 12th 2009, 03:48 PM
Barthayn
Quote:

Originally Posted by Volcanicrain
How do I isolate x here?
48.99 = 36.34(1+x)^2 + ([(1+x)^2 - 1]/x)

I get to:
(1+x)^2 = (48.99x + 1)/(36.34x + 1)
But I can't simplify my equation further.

Also, x > 0. I know x = 0.1355 but I can't get to it algebraically.

$48.99 = 36.34(1+x)^2 + ([(1+x)^2 - 1]/x)$
$48.99 = 36.34(x^2+2x+1) + ([(1+x)^2 - 1]/x)$
$48.99 = 36.34x^2 + 72.68x + 36.34 + (x^2 + 2x / x)$
$48.99x = 36.34x^2 + 72.68x + 36.34 + x^2 + 2x$
$48.99x = 37.34x^2 + 74.68x + 36.34$
$-25.69x = 37.34x^2 + 36.34$
$-25.69x = 6.11x + 36.34$
$-31.8x = 36.34$
$x = -1.14$

Does this help?
• Oct 12th 2009, 03:53 PM
Volcanicrain
Quote:

Originally Posted by Raoh
$\frac{(1+x)^{2}(36.34x+1)-(48.99x+1)}{36.34x+1}=0$ $\Leftrightarrow 36.34 x^3+73.68 x^2-10.65 x=0$ solve for $x$ ,you'll get $x=0.13549$ for $x> 0$

Thank you!
Just a quick question - I can ignore the denominator in this case right? As long as the denominator is not equal to 0, then the equation will be satisfied.

Thanks a ton!

Thanks Barthayn too, but I believe you forgot to multiply an x in the middle.
• Oct 12th 2009, 03:56 PM
Raoh
Quote:

Originally Posted by Volcanicrain
Thank you!
Just a quick question - I can ignore the denominator in this case right? As long as the denominator is not equal to 0, then the equation will be satisfied.

Thanks a ton!

Thanks Barthayn too, but I believe you forgot to multiply an x in the middle.

yes(Happy)
• Oct 12th 2009, 09:58 PM
Wilmer
Quote:

Originally Posted by Volcanicrain
How do I isolate x here?
48.99 = 36.34(1+x)^2 + ([(1+x)^2 - 1]/x)

Try it like this (just a suggestion):

Let a = 48.99 and b = 36.34

a - b(1 + x)^2 = [(1 + x)^2 - 1] / x

ax - bx(1 + x)^2 = (1 + x)^2 - 1

ax - bx(1 + x)^2 = x^2 + 2x

a - b(1 + x)^2 = x + 2

Carry on...