How would you solve 23.585 = x/1.05 + (x/1.055)^2 ?

I don't know why I'm having a hard time with this...

23.585 = (x/1.05) + (x/(1.055)[sup:1umgmvrm]2[/sup:1umgmvrm])

I know the answer is x=12.74, but I can't follow the steps.

Any help would be greatly appreciated. Thanks

Re: How would you solve this?

You will need a good calculator.

\(\displaystyle 23.585 =\frac{x}{1.05}+\frac{x}{1.055^2}\)

Multiply both sides by 1.055[sup:1h1jph20]2[/sup:1h1jph20] giving you

\(\displaystyle 23.585(1.055)^2=\frac{1.055^2x}{1.05}+x\)

Now, you have to do the arithmetic and combine the two x terms.

Following those steps my answer was x=12.74290836.

\(\displaystyle 23.585 = \frac{x}{1.05} + \frac{x}{1.055^2}\)

\(\displaystyle 23.585 = x \left(\frac{1}{1.05} + \frac{1}{1.055^2}\right)\)

\(\displaystyle \frac{23.585}{ \left(\frac{1}{1.05} + \frac{1}{1.055^2}\right)} = x\)

Let a = 1.05, b = 1.055^2

x/a + x/b = 23.585
(bx + ax) / (ab) = 23.585
x(a + b) = 23.585ab
x = 23.585ab / (a + b)