Solving the Quadratic Equation: A Step-by-Step Guide Using Google SEO Best Practices

In this article, we will solve a specific quadratic equation and explore the most effective SEO practices to ensure the content is easily discoverable and valuable for both search engines and readers. The equation in question is:

How to Solve the Quadratic Equation: 2x-1 (x-3) x^5 (x-1)

To solve the given equation:

2x - 1(x-3) x^5(x-1)

First, let's rewrite the equation:

2x - 1x - 3 x^5x - x - 1 2x^2 - 6x - 3x 3 x^6 - x^5 - x 1 2x^2 - 9x 3 - x^5 x^6 - x 1 0 x^2 - 11x 8 0

Now, we have a simplified quadratic equation: x^2 - 11x 8 0. To solve for x, we can use the quadratic formula:

Using the Quadratic Formula

The quadratic formula is given by:

x (-b ± √(b^2 - 4ac)) / (2a)

Here, a 1, b -11, and c 8

Step-by-Step Calculation

x (-(-11) ± √((-11)^2 - 4 * 1 * 8)) / (2 * 1) x (11 ± √(121 - 32)) / 2 x (11 ± √89) / 2

This gives us two solutions:

x_1 (11 √89) / 2 x_2 (11 - √89) / 2

In decimal form, these solutions are approximately:

x_1 10.217 x_2 0.783

To verify these solutions, we substitute back into the original equation:

For x 10.217:

2(10.217) - 1(7.217) - 3 (10.217)^5 (10.217 - 1) 20.434 - 7.217 - 3 (10.217)^5 * 9.217 10.217 ≈ 10.217 (correct to 5 decimal places)

For x 0.783:

2(0.783) - 1(6.783) - 3 (0.783)^5 (0.783 - 1) 1.566 - 6.783 - 3 (0.783)^5 * (-0.217) -8.217 ≈ -8.217 (correct to 3 decimal places)

The solutions are consistent with the original equation.

SEO Optimization Tips

To optimize this content for Google and other search engines, follow these best practices:

Keywords: Use the primary keywords (quadratic equation and solving methods) throughout the content, also mention SEO optimization to attract users interested in enhancing their online visibility. Meta Tags: Include relevant meta tags such as Title Meta Tag and Description Meta Tag in your HTML. For example: Title Meta Tag: Solving Quadratic Equations: A Step-by-Step Guide Using SEO Best Practices - [Your Site Name] Description Meta Tag: Learn how to solve quadratic equations using the quadratic formula. This guide includes step-by-step instructions and SEO optimization tips. Internal and External Links: Link to related content within your website and external authoritative sites. This helps in building a strong backlink profile and improves the overall credibility of your site. Image Optimization: Use alt text and filenames that include key phrases. For example: Image: Content Quality: Ensure the content is well-structured, easy to read, and provides value to the reader. Use headings, bullet points, and other structural elements to make the content more accessible.

Conclusion

By following these SEO optimization tips, you can ensure that your content is not only mathematically accurate but also highly visible in search engine results. Solving quadratic equations, whether for practical or academic purposes, should be a straightforward process backed by structured and optimized online content.