SOLUTION: 0 = 5(x^3) + 10 + 10(x^2) solve for x? or factor?

Question 29300: 0 = 5(x^3) + 10 + 10(x^2)
solve for x? or factor?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
Not too sure how to approach this apart from a numerical one... We have . This does not factorise easily.

Approach is:
pick value of x
find the value of y
pick another value of x
when sign of y changes, we have "straddled" the solution, the root, the answer.
we then look at a more precise value of x and repeat the process.

So,
start with x=-1... --> -1 + 2 + 2 --> +ve
now, try x = -2... --> -8 + 8 + 2 --> +ve but getting closer to zero
now try x = -3... --> -27 + 18 + 2 --> -ve

So the root lies between x=-2 and x=-3.

Now pick x=-2.5... --> -ve, so the root lies between x=-2 and x=-2.5

So, pick x=-2.4... --> -ve, Just. The root lies between x=-2 and x=-2.4

Pick x=-2.3... --> +ve, so the root lies now between x=-2.3 and x=-2.4.

So now you try say x=-2.35 and work out the bounds of the root etc.

Looking at the graph, we do indeed see a solution between -2 and -3.

is a closer look at the root.
jon

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