How do you find x if 4x power 3 plus 50x equals 250?

Answer 1

Cubic and higher polynomials are difficult to solve; you can use Excel Solver to do it for you, or a Web site like Wolframalpha. On this site, type the input as: solve 4x^3 + 50x = 250. Here is the result:

http://www.wolframalpha.com/input/?i=solve+4x^3+%2B+50x+=+250

As you can see, the equation has one real solution, and two complex solutions.

If you want to solve it yourself:

Put the 250 to the left:

4x3 + 50x - 250 = 0

Divide by 2:

2x3 + 25x - 125 = 0

Any rational root (solution) of this has a numerator that is a factor of 125 (options are 1, -1, 5, -5, 25, -25, 125, -125), and a denominator that is a factor of 2 (1, -1, 2, -2). This gives you a total of 14 combinations.

In this case, that won't work (since the solutions are not rational). The easiest method is to try different numbers for "x", until you get close to a solution.