Answer:
x = 3∛(3) / ∛(2).
Explanation:
Start by adding 27 to both sides of the equation to isolate the term with x^3 on the left side:
2x^3 = 27
Next, divide both sides by 2 to solve for x^3:
x^3 = 27 / 2
Now, take the cube root of both sides to find the value of x:
x = ∛(27 / 2)
x = ∛(27) / ∛(2)
Simplify the cube root of 27:
x = 3∛(3) / ∛(2)
So, the x-values for which 2x^3 - 27 equals zero are x = 3∛(3) / ∛(2).