Let's solve the equation \( x \cdot x \cdot x + x = 30 \).

1. Start by rewriting the equation:
   \[
   x^3 + x = 30
   \]

2. Subtract 30 from both sides to set the equation to zero:
   \[
   x^3 + x - 30 = 0
   \]

3. Now, we'll solve for \( x \). This is a cubic equation, so we can look for possible rational roots by testing values.

4. Testing \( x = 3 \):
   \[
   3^3 + 3 = 27 + 3 = 30
   \]
   So, \( x = 3 \) is a solution.

Therefore, the solution to the equation is \( x = 3 \).

Would you like more details or have any questions? Here are some related questions:

1. What is a cubic equation?
2. How can you solve a cubic equation if no simple root is apparent?
3. What are the methods for solving cubic equations algebraically?
4. How do you factor a cubic polynomial?
5. Can cubic equations have more than one real solution?
6. What is the Rational Root Theorem?
7. How does synthetic division help in solving polynomial equations?
8. How do you graph a cubic function?

**Tip:** When solving polynomial equations, always test simple integer values like -1, 0, 1, 2, and 3 for potential roots.

Learn how to solve the cubic equation x^3 + x = 30 with a detailed step-by-step solution. This problem covers key algebraic concepts, including cubic equations, root finding methods, and the application of the Rational Roots Theorem. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation