To solve the equation $(x + 6)^3 = 4$, let's go through each step.

Step 1: Take the cube root of both sides

$x + 6 = \sqrt[3]{4}$

Step 2: Solve for $x$

Subtract 6 from both sides: $x = \sqrt[3]{4} - 6$

Final Answer:

$x = \sqrt[3]{4} - 6$ or approximately: $x \approx -4.368$

Would you like additional details on any step?

Related Questions:

1. How do we calculate cube roots of non-integer values?
2. How would the solution change if the exponent were different, such as $(x + 6)^2 = 4$?
3. What if the equation were $(x + 6)^3 = -4$?
4. How do we solve for $x$ if given $(x - 2)^3 = 5$?
5. What does it mean for a function to have an inverse, such as finding $x$ from a cubed term?

Tip:

Remember that taking the cube root can result in only one real solution for equations of this type.