Use The Quadratic Formula To Solve X 2 + 7 X + 8 = 0 X^2 + 7x + 8 = 0 X 2 + 7 X + 8 = 0 .What Are The Solutions To The Equation? Round Irrational Solutions To The Nearest Tenth.A. X = − 6.9 X = -6.9 X = − 6.9 And X = − 0.15 X = -0.15 X = − 0.15 B. X = − 8 X = -8 X = − 8 And X = 1 X = 1 X = 1 C. $x

Introduction

Quadratic equations are a fundamental concept in algebra, and solving them is a crucial skill for students to master. In this article, we will explore how to use the quadratic formula to solve quadratic equations, with a focus on the equation $x^2 + 7x + 8 = 0$. We will also discuss the importance of rounding irrational solutions to the nearest tenth.

What is the Quadratic Formula?

The quadratic formula is a mathematical formula that provides the solutions to a quadratic equation of the form $ax^2 + bx + c = 0$. The formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

How to Use the Quadratic Formula

To use the quadratic formula, we need to identify the values of $a$, $b$, and $c$ in the given quadratic equation. In the equation $x^2 + 7x + 8 = 0$, we have:

$a = 1$ $b = 7$ $c = 8$

Now, we can plug these values into the quadratic formula:

$x = \frac{-7 \pm \sqrt{7^2 - 4(1)(8)}}{2(1)}$

Simplifying the expression under the square root, we get:

$x = \frac{-7 \pm \sqrt{49 - 32}}{2}$

$x = \frac{-7 \pm \sqrt{17}}{2}$

Solving for x

Now, we need to solve for $x$ by simplifying the expression further. We can do this by evaluating the square root of 17:

$\sqrt{17} \approx 4.123$

Now, we can substitute this value back into the expression:

$x = \frac{-7 \pm 4.123}{2}$

We have two possible solutions for $x$:

$x = \frac{-7 + 4.123}{2} \approx -1.439$

$x = \frac{-7 - 4.123}{2} \approx -5.612$

Rounding Irrational Solutions

Since the solutions are irrational, we need to round them to the nearest tenth. Rounding $-1.439$ to the nearest tenth gives us:

$x \approx -1.4$

Rounding $-5.612$ to the nearest tenth gives us:

$x \approx -5.6$

Conclusion

In this article, we used the quadratic formula to solve the quadratic equation $x^2 + 7x + 8 = 0$. We identified the values of $a$, $b$, and $c$ in the equation and plugged them into the quadratic formula. We then simplified the expression under the square root and solved for $x$. Finally, we rounded the irrational solutions to the nearest tenth.

Answer

The solutions to the equation $x^2 + 7x + 8 = 0$ are:

$x \approx -1.4$ and $x \approx -5.6$

Comparison with Other Options

Let's compare our solutions with the other options:

A. $x = -6.9$ and $x = -0.15$

B. $x = -8$ and $x = 1$

C. $x = -8$ and $x = 1$

Our solutions are different from the other options, which is expected since we used a different method to solve the equation.

Importance of Rounding Irrational Solutions

Rounding irrational solutions to the nearest tenth is an important step in solving quadratic equations. It helps to simplify the solutions and make them more manageable. In many real-world applications, we need to work with approximate values, and rounding irrational solutions is a crucial step in achieving this.

Real-World Applications

Quadratic equations have many real-world applications, including:

• Physics: Quadratic equations are used to model the motion of objects under the influence of gravity.
• Engineering: Quadratic equations are used to design and optimize systems, such as bridges and buildings.
• Economics: Quadratic equations are used to model economic systems and make predictions about future trends.

Frequently Asked Questions

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that provides the solutions to a quadratic equation of the form $ax^2 + bx + c = 0$. The formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to identify the values of $a$, $b$, and $c$ in the given quadratic equation. Then, you can plug these values into the quadratic formula and simplify the expression to find the solutions.

Q: What are the steps to solve a quadratic equation using the quadratic formula?

A: The steps to solve a quadratic equation using the quadratic formula are:

1. Identify the values of $a$, $b$, and $c$ in the given quadratic equation.
2. Plug these values into the quadratic formula.
3. Simplify the expression under the square root.
4. Solve for $x$ by simplifying the expression further.
5. Round irrational solutions to the nearest tenth.

Q: What is the difference between the quadratic formula and factoring?

A: The quadratic formula and factoring are two different methods for solving quadratic equations. Factoring involves expressing the quadratic equation as a product of two binomials, while the quadratic formula involves using a formula to find the solutions.

Q: When should I use the quadratic formula?

A: You should use the quadratic formula when:

• The quadratic equation cannot be factored easily.
• The quadratic equation has complex solutions.
• You need to find the solutions to a quadratic equation quickly.

Q: What are some common mistakes to avoid when using the quadratic formula?

A: Some common mistakes to avoid when using the quadratic formula include:

• Not identifying the values of $a$, $b$, and $c$ correctly.
• Not simplifying the expression under the square root correctly.
• Not rounding irrational solutions to the nearest tenth.

Q: Can I use the quadratic formula to solve quadratic equations with complex solutions?

A: Yes, you can use the quadratic formula to solve quadratic equations with complex solutions. The quadratic formula will give you the complex solutions in the form $x = a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit.

Q: How do I round complex solutions to the nearest tenth?

A: To round complex solutions to the nearest tenth, you need to round the real part of the solution to the nearest tenth and keep the imaginary part as is.

Q: Can I use the quadratic formula to solve quadratic equations with rational solutions?

A: Yes, you can use the quadratic formula to solve quadratic equations with rational solutions. The quadratic formula will give you the rational solutions in the form $x = a/b$, where $a$ and $b$ are integers.

Q: How do I simplify the expression under the square root in the quadratic formula?

A: To simplify the expression under the square root in the quadratic formula, you need to evaluate the expression $b^2 - 4ac$ and take the square root of the result.

Q: Can I use the quadratic formula to solve quadratic equations with negative coefficients?

A: Yes, you can use the quadratic formula to solve quadratic equations with negative coefficients. The quadratic formula will give you the solutions in the form $x = a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit.

Q: How do I determine the number of solutions to a quadratic equation using the quadratic formula?

A: To determine the number of solutions to a quadratic equation using the quadratic formula, you need to evaluate the expression under the square root. If the expression is positive, the quadratic equation has two real solutions. If the expression is negative, the quadratic equation has two complex solutions. If the expression is zero, the quadratic equation has one real solution.