To solve the equation \( 5x^2 \cdot 18x + 16 = 0 \), we will first simplify and then solve for \( x \).

1. **Simplify the equation**:
   \[
   5x^2 \cdot 18x + 16 = 90x^3 + 16 = 0
   \]

   The equation is a cubic equation.

2. **Isolate the cubic term**:
   \[
   90x^3 = -16
   \]

3. **Solve for \( x^3 \)**:
   \[
   x^3 = \frac{-16}{90} = \frac{-8}{45}
   \]

4. **Solve for \( x \)** by taking the cube root of both sides:
   \[
   x = \sqrt[3]{\frac{-8}{45}}
   \]

   This is the exact solution.

To express the solution more simply:
   \[
   x \approx -0.258
   \]

This is the approximate decimal form of the solution.

Would you like more details on solving cubic equations, or do you have any other questions?

---

Here are 8 related questions for further practice:

1. How do you solve \( 4x^3 + 8 = 0 \)?
2. What are the solutions for \( x^3 - 27 = 0 \)?
3. How do you factor a cubic equation?
4. How do you solve \( 2x^2 \cdot 5x + 3 = 0 \)?
5. What is the general form of a cubic equation?
6. How do you solve \( x^3 + 8x^2 - 5x - 40 = 0 \) using synthetic division?
7. How do you determine the nature of roots for cubic equations?
8. Can you solve \( 3x^2 + 12x + 7 = 0 \) using the quadratic formula?

**Tip:** When dealing with cubic equations, check if they can be factored into a quadratic and linear term, which simplifies the solving process.

Learn how to solve the cubic equation 5x^2 * 18x + 16 = 0 with a detailed step-by-step solution. This problem involves simplifying cubic equations, isolating cubic terms, solving for x, and interpreting solutions. 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