Stuck on an algebra ?

[panamarojo1989]

Hello everyone,

I am currently taking finance, we mostly work off excel and financial calculators. A particular question came up that involved adding fractions with different squared variables in the denominator and I got stuck! I used to be so good at this stuff LOL.

Attached is the problem, the original problem is highlighted green, the red highlight is how I approached the problem.

If anyone can help me I'd be highly appreciative.

Answer is supposedly x = 17.71%, I'm just curious about the algebra.

Thanks!

 

[Cubist]

I suspect there is more to this question than given, because you give a percentage answer. If you can show the original question it might help us to guide you.

A solution is approximately x ≈1.1771

Would you be expected to solve a cubic on your course? Or would you be expected to use a spreadsheet to solve this problem?

 

[HallsofIvy]

I would start by multiplying both sides of the equation by \(\displaystyle x^3\): \(\displaystyle 28200x^3= 12200x^2+ 15200x+ 11200\)

An obvious simplification is to divide by 100;
\(\displaystyle 282x^3= 122x^3+ 152x+ 112\)

And since all of those numbers are even, divide by 2:
\(\displaystyle 141x^3= 61x^2+ 76x+ 56\).

Shift all the numbers to the left:
\(\displaystyle 141x^3- 61x^2- 76x- 56= 0\)

There are formulas for solving general cubic equations but they are extremely complicated.

The Cubic Formula

You might prefer a numerical method

Newton's method - Wikipedia

en.wikipedia.org

 

[Cubist]

By the way, looking at your work in red, there isn't much point in factoring part of an equation in this form. Factoring the RHS can really help if the LHS is zero, but in your case it isn't. For example if you are starting with:-

0 = 56y³ + 76y² + 61y

then it is great to do the following

0 = y * ( 56y² + 76y + 61 )

because this tells you that y=0 is a solution (and you're then just left with a quadratic in the brackets)

--

However if you're starting with:-

141 = 56y³ + 76y² + 61y

then doing this is a bit pointless

141 = y * ( 56y² + 76y + 61 )

because y=0 is not a solution to the above. So you'd really need to bring the 141 to the RHS and then factor something from the whole of the RHS

0 =56y³ + 76y² + 61y - 141

0 =(y - ?) * ( ? y² + ? y + ? ) where ? numbers are to be determined, which is hard because the line above is a cubic

 

[panamarojo1989]

I attached the original question, along with a solution I found on Chegg. Only there is no work provided on how the answer of 17.77% was obtained.

 

[Steven G]

What is the IRR rule??