Consider The Equation 6 − 4 X 3 = − 494 6 - 4x^3 = -494 6 − 4 X 3 = − 494 .a. What Is The Value Of − 4 X 3 -4x^3 − 4 X 3 ?b. What Is The Value Of X 3 X^3 X 3 ?c. What Is The Value Of X X X ?

In this article, we will delve into the world of cubic equations and explore the solution to the given equation $6 - 4x^3 = -494$. We will break down the problem into manageable steps, making it easier to understand and solve.

Understanding the Equation

The given equation is a cubic equation, which means it contains a variable raised to the power of 3. The equation is $6 - 4x^3 = -494$. Our goal is to solve for the value of $x$.

Step 1: Isolate the Cubic Term

To begin solving the equation, we need to isolate the cubic term. We can do this by adding $4x^3$ to both sides of the equation.

6 - 4x^3 + 4x^3 = -494 + 4x^3

This simplifies to:

6 = 4x^3 - 494

Step 2: Add 494 to Both Sides

Next, we add 494 to both sides of the equation to get rid of the negative term.

6 + 494 = 4x^3 - 494 + 494

This simplifies to:

500 = 4x^3

Step 3: Divide by 4

Now, we divide both sides of the equation by 4 to isolate the cubic term.

\frac{500}{4} = \frac{4x^3}{4}

This simplifies to:

125 = x^3

Step 4: Take the Cube Root

To find the value of $x$, we need to take the cube root of both sides of the equation.

\sqrt[3]{125} = \sqrt[3]{x^3}

This simplifies to:

5 = x

Conclusion

In this article, we solved the cubic equation $6 - 4x^3 = -494$ by following a step-by-step approach. We isolated the cubic term, added 494 to both sides, divided by 4, and finally took the cube root to find the value of $x$. The final answer is $x = 5$.

What is the Value of $-4x^3$?

To find the value of $-4x^3$, we can substitute the value of $x^3$ into the equation.

-4x^3 = -4(125)

This simplifies to:

-4x^3 = -500

What is the Value of $x^3$?

We already found the value of $x^3$ in Step 3.

x^3 = 125

What is the Value of $x$?

We already found the value of $x$ in Step 4.

x = 5

Final Answer

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In this article, we will address some of the most common questions related to solving cubic equations. Whether you're a student, a teacher, or simply someone who wants to learn more about cubic equations, this FAQ section is for you.

Q: What is a cubic equation?

A: A cubic equation is a polynomial equation of degree three, which means it contains a variable raised to the power of three. The general form of a cubic equation is $ax^3 + bx^2 + cx + d = 0$, where $a$, $b$, $c$, and $d$ are constants.

Q: How do I solve a cubic equation?

A: Solving a cubic equation can be a bit challenging, but it's definitely doable with the right steps. Here's a general outline:

1. Isolate the cubic term by adding or subtracting terms from both sides of the equation.
2. Add or subtract a constant to both sides of the equation to get rid of the negative term.
3. Divide both sides of the equation by a common factor to simplify the equation.
4. Take the cube root of both sides of the equation to find the value of $x$.

Q: What is the difference between a cubic equation and a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means it contains a variable raised to the power of two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. In contrast, a cubic equation is a polynomial equation of degree three, which means it contains a variable raised to the power of three.

Q: Can I use the quadratic formula to solve a cubic equation?

A: No, you cannot use the quadratic formula to solve a cubic equation. The quadratic formula is used to solve quadratic equations, not cubic equations. To solve a cubic equation, you need to use a different approach, such as the one outlined above.

Q: What is the significance of the cube root in solving cubic equations?

A: The cube root is a crucial step in solving cubic equations. By taking the cube root of both sides of the equation, you can find the value of $x$ that satisfies the equation.

Q: Can I use a calculator to solve a cubic equation?

A: Yes, you can use a calculator to solve a cubic equation. In fact, many calculators have built-in functions for solving cubic equations. However, it's always a good idea to understand the underlying math and the steps involved in solving the equation.

Q: What are some common mistakes to avoid when solving cubic equations?

A: Here are some common mistakes to avoid when solving cubic equations:

• Not isolating the cubic term correctly
• Not adding or subtracting a constant to both sides of the equation
• Not dividing both sides of the equation by a common factor
• Not taking the cube root of both sides of the equation

Q: Can I use the same approach to solve all types of cubic equations?

A: No, you cannot use the same approach to solve all types of cubic equations. Depending on the specific equation, you may need to use different techniques or approaches to solve it.

Q: Where can I find more resources on solving cubic equations?

A: There are many resources available online and in textbooks that can help you learn more about solving cubic equations. Some popular resources include:

• Online math tutorials and videos
• Math textbooks and workbooks
• Online forums and discussion groups
• Math software and calculators

Conclusion

Solving cubic equations can be a bit challenging, but with the right approach and resources, you can master it. Remember to isolate the cubic term, add or subtract a constant, divide by a common factor, and take the cube root to find the value of $x$. If you have any more questions or need further clarification, feel free to ask!