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.

Discover the step-by-step solution to solve the cubic equation (x+6)^3=4. This guide covers core algebraic concepts, such as cube roots and radical operations, ideal for high school students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation