SOLUTION: Hi! On the following problem I keep getting the incorrect answer. I think I'm close to the right answer just making a small error somewhere. Can you help me? Solve the equati

You can put this solution on YOUR website!
The constant a represents a positive real number.
a^3x^3 + 64 = 0
(ax+4)*(a^2x^2 - 4ax + 16) = 0
x = -4/a
---------

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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 -48 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 -48 is + or - . The solution is , or Here's your graph:

----------------
Reducing gives:
2 ± isqrt(12)
Then taking the "a" into account:
x = (2 ± 2i*sqrt(3))/a

You can put this solution on YOUR website!
Start with the given equation.


Rewrite as


Rewrite as


Factor the left side using the sum of cubes formula


Recall, the sum of cubes formula is


Multiply and simplify


or Use the zero product property to break up the factors


-----------------------------------------------------

Let's solve the first equation:


Start with the first equation.


Subtract 4 from both sides.


Divide both sides by "a" to isolate "x".


So the first solution is

-----------------------------------------------------

Now let's solve the second equation:


Start with the second equation.


Notice we have a quadratic in the form of where , , and


Let's use the quadratic formula to solve for "x"


Start with the quadratic formula


Plug in , , and


Negate -4a to get 4a


Square -4a to get


Multiply


Combine like terms.


Factor -48 into


Break up the square root.


Simplify the square roots and replace with "i".


Note:


Rearrange the terms.


or Break up the "plus/minus"


or Reduce


So the next two solutions are or


================================================

Answer:

So the three solutions are , or