x 2 4x 2 0

Guri Bee

less than a minute read

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20-10-2024

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Solving Quadratic Equations: A Step-by-Step Guide

This article will explore how to solve the quadratic equation: x² + 4x² = 0. We'll break down the steps involved, providing explanations and practical examples to help you understand the concepts.

Understanding the Equation

The equation x² + 4x² = 0 is a quadratic equation. It has the general form ax² + bx + c = 0, where 'a', 'b', and 'c' are coefficients. In our equation:

• a = 1 (since x² is the same as 1x²)
• b = 0 (as there's no 'x' term)
• c = 0

Step 1: Simplifying the Equation

First, we can combine like terms:

x² + 4x² = 5x²

This simplifies the equation to 5x² = 0

Step 2: Isolating the Variable

To solve for x, we need to isolate the x² term. We can do this by dividing both sides of the equation by 5:

(5x²) / 5 = 0 / 5

This simplifies to x² = 0

Step 3: Solving for x

Now, to get rid of the square, we take the square root of both sides of the equation:

√(x²) = √0

This gives us x = 0

Solution

The solution to the equation x² + 4x² = 0 is x = 0.

Key Concepts

• Quadratic Equation: An equation of the form ax² + bx + c = 0.
• Simplifying: Combining like terms to make the equation easier to work with.
• Isolating the Variable: Getting the variable term by itself on one side of the equation.
• Square Root: The inverse operation of squaring.

Practical Example

Imagine you are building a rectangular garden. You know that the length is twice the width. You also know that the area of the garden is 0 square units. Using the formula for the area of a rectangle (Area = length * width), we can set up an equation:

2w * w = 0

This simplifies to 2w² = 0

Solving for w (width), we get w = 0. This means the garden has zero width, and therefore, no area.

Conclusion

Solving quadratic equations is a fundamental skill in algebra. Understanding the steps involved and applying them to real-world problems allows you to solve for unknown variables and gain insights into various situations. By following the process outlined in this article, you can confidently tackle quadratic equations and their applications.