The First Few Steps In Solving The Quadratic Equation $8x^2 + 80x = -5$ By Completing The Square Are Shown:1. $8x^2 + 80x = -5$2. $8(x^2 + 10x) = -5$3. $8(x^2 + 10x + 25) = -5 + \quad \, \, $Which Number Is Missing

**The First Few Steps in Solving the Quadratic Equation: A Step-by-Step Guide** ===========================================================

Introduction

Solving quadratic equations is a fundamental concept in mathematics, and one of the most effective methods is completing the square. In this article, we will explore the first few steps in solving the quadratic equation $8x^2 + 80x = -5$ by completing the square.

The Quadratic Equation

The given quadratic equation is $8x^2 + 80x = -5$. To solve this equation, we will use the method of completing the square.

Step 1: Factor out the coefficient of $x^2$

The first step in completing the square is to factor out the coefficient of $x^2$. In this case, the coefficient of $x^2$ is 8.

8x^2 + 80x = -5

We can factor out 8 from the first two terms:

8(x^2 + 10x) = -5

Step 2: Find the number to add inside the parentheses

To complete the square, we need to find a number that, when added inside the parentheses, will make the expression a perfect square trinomial. In this case, we need to add $(10/2)^2 = 25$ inside the parentheses.

8(x^2 + 10x + 25) = -5 + 8(25)

Step 3: Simplify the right-hand side

Now, we can simplify the right-hand side of the equation:

8(x^2 + 10x + 25) = -5 + 200

Step 4: Combine like terms

Finally, we can combine like terms on the right-hand side:

8(x^2 + 10x + 25) = 195

Q&A

Q: What is the missing number in the equation?

A: The missing number is 25.

Q: Why do we need to factor out the coefficient of $x^2$?

A: We need to factor out the coefficient of $x^2$ to make it easier to complete the square.

Q: How do we find the number to add inside the parentheses?

A: We find the number to add inside the parentheses by taking half of the coefficient of $x$ and squaring it.

Q: What is the final result of completing the square?

A: The final result of completing the square is a perfect square trinomial on the left-hand side and a simplified expression on the right-hand side.

Conclusion

In this article, we have explored the first few steps in solving the quadratic equation $8x^2 + 80x = -5$ by completing the square. We have factored out the coefficient of $x^2$, found the number to add inside the parentheses, simplified the right-hand side, and combined like terms. The missing number in the equation is 25. We hope this article has provided a clear and concise guide to completing the square.

Frequently Asked Questions

Q: What is completing the square?

A: Completing the square is a method of solving quadratic equations by transforming the equation into a perfect square trinomial.

Q: Why is completing the square useful?

A: Completing the square is useful because it allows us to solve quadratic equations that cannot be factored easily.

Q: How do I know when to use completing the square?

A: You should use completing the square when the quadratic equation cannot be factored easily or when you need to find the vertex of a parabola.

Q: Can I use completing the square to solve all types of quadratic equations?

A: No, completing the square is only useful for quadratic equations that can be written in the form $ax^2 + bx + c = 0$.

Additional Resources

For more information on completing the square, please see the following resources:

• Khan Academy: Completing the Square
• Mathway: Completing the Square
• Wolfram Alpha: Completing the Square

We hope this article has provided a clear and concise guide to completing the square. If you have any further questions or need additional help, please don't hesitate to ask.