SOLUTION: I'm supposed to find the solutions of x for the equation: 27x^3=(x+5)^3 I tried using the difference of cubes where a=(x+5)^3 and b=27x^3 but running through it gave a polyno

Question 632223: I'm supposed to find the solutions of x for the equation:
27x^3=(x+5)^3
I tried using the difference of cubes where a=(x+5)^3 and b=27x^3 but running through it gave a polynomial to the 6th power, which doesn't do me much good. Please help.
Found 3 solutions by reviewermath, solver91311, Earlsdon:
Answer by reviewermath(1029)   (Show Source): You can put this solution on YOUR website!
Using the difference of two cubes where and .

or
Solve:

Solve:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -675 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -675 is + or - .

The solution is

Here's your graph:

There is only one real solution, x = 5/2.
The other two roots are imaginary numbers as computed above.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Your error, I think, was stating that and when in fact you should have started with and , which would lead you to and

Then using the pattern to write:

You can take it from here. You should get a linear binomial factor and a quadratic trinomial on which you will need to use the quadratic formula. The net result will be one real root and a pair of complex conjugates.

John

My calculator said it, I believe it, that settles it

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Try a simpler approach:
Rewrite as:
Take the cube root of both sides.
Subtract x from both sides.
Finally, divide both sides by 2.

RELATED QUESTIONS
I need to factor 27x^3 - 8y^3 using the difference of two cubes... (answered by nerdybill)
Find the three solutions to x^3=8 I've already factored it using the difference of cubes (answered by MathTherapy)
The problem is 8x^3=125. Why can't I simply take the cubed root of both sides to get... (answered by ikleyn,MathTherapy,greenestamps)
Find all real solutions of the equation.... (answered by richwmiller)
I am supposed to find the product of this polynomial equation and I need some help.... (answered by Alan3354)
Roots A.)Find each root - sq root 25 B) Quotient Rule for Radicals Simplify... (answered by solver91311)
I believe this would be the best place to ask...Okay, this is a relation (set of... (answered by venugopalramana)
I am having a difficult time answering this question, using the difference of cubes can... (answered by solver91311)
use your factoring skills to find all the solutions for x . express complex roots in... (answered by Alan3354,doodles)