hi,

i nned to solve this equation:

x^3-5x=8

x=2.7

im unsure how to work this out.

i know i would do 2.7^3-13.5x=8 but i don't know what to do after this.

some help would be great!

thanks!

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- May 5th 2011, 08:16 AMandyboy179solve the equation
hi,

i nned to solve this equation:

x^3-5x=8

x=2.7

im unsure how to work this out.

i know i would do 2.7^3-13.5x=8 but i don't know what to do after this.

some help would be great!

thanks! - May 5th 2011, 10:17 AMSpringFan25
2.7 is not a solution to the equation you posted. did you type it correctly?

**edit**incorrect comment removed, oops. - May 5th 2011, 10:17 AMSambit
Let so that you have to find a value of that satisfies the equation . Observe that and . So there lies x , (where ,) such that f(x)=0.

See that . So for to be , you have .

After this take so on and notice when changes its sign. After afew couple of steps you will get the solution according to what precision you want to maintain.

However, the correct solution is - May 5th 2011, 01:31 PMandyboy179
springfan25- yes i have to find if 2.7 works or not and the second part is 2.8 but i was going to do that on my own.

sambit- i don't really understand what you have written. could i -8 from each side to get 2.7^3-13.5x-8=0 and do a quadratic equation? - May 5th 2011, 01:35 PMpoirot
This is a cubic equation so no you could not 'do a quadratic equation'. I assume you are doing numerical methods. In which case the bisection method outlined by Sambit could be used.

- May 5th 2011, 01:40 PMandyboy179
- May 5th 2011, 10:03 PMSambit
To begin with, think in simple way. and are equivalent. Aren't they? So here solving is equivalent to solving . Alright? You are just subtracting from both the sides; so they must be equivalent.

Next try to understand what does a*solution of an equation*mean. I suppose you have the preliminary concept regarding function and graph. If you are gievn a function (for example, here you have ), plot in a graph ( that is, put values of along horizontal X-axis and values of along vertical Y-axis). The function will have a solution at if is at (that is ). In this case, your function looks like THIS. The blue line denotes . Notice that as increases, increases ( becomes +ve from -ve). During this increase, the curve cuts the X-axis at some point (red point)-- that particular point is the solution of your equation.

So this is the concept. This is why you should find two consecutive values of such that and , because your required solution always lies in between and

Now I hope you'll understand what my previous post meant.

The red point is the solution: 2.80259