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 = − 5.6 X = -5.6 X = − 5.6 And X = − 1.4 X = -1.4 X = − 1.4 C.

Introduction

Quadratic equations are a fundamental concept in mathematics, and they can be solved using various methods, including factoring, completing the square, and the quadratic formula. In this article, we will focus on using the quadratic formula to solve a quadratic equation. The quadratic formula is a powerful tool that can be used to find the solutions to any quadratic equation in the form of $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

The Quadratic Formula

The quadratic formula is given by:

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

This formula can be used to find the solutions to any quadratic equation in the form of $ax^2 + bx + c = 0$. The formula consists of two parts: the first part is the negative of the coefficient of the linear term ($-b$), and the second part is the square root of the discriminant ($\sqrt{b^2 - 4ac}$).

Solving the Equation

Now, let's use the quadratic formula to solve the equation $x^2 + 7x + 8 = 0$. To do this, we need to identify the values of $a$, $b$, and $c$ in the equation. In this case, $a = 1$, $b = 7$, and $c = 8$.

Step 1: Plug in the values of a, b, and c

We will now plug in the values of $a$, $b$, and $c$ into the quadratic formula:

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

Step 2: Simplify the expression

We will now simplify the expression inside the square root:

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

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

Step 3: Simplify the square root

We will now simplify the square root:

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

Step 4: Find the two solutions

We will now find the two solutions by plugging in the positive and negative values of the square root:

$$x_1 = \frac{-7 + 4.123}{2} = -1.439$$

$$x_2 = \frac{-7 - 4.123}{2} = -5.612$$

Rounding Irrational Solutions

Since the problem asks us to round irrational solutions to the nearest tenth, we will round the solutions to the nearest tenth:

$$x_1 = -1.4$$

$$x_2 = -5.6$$

Conclusion

In this article, we used the quadratic formula to solve the 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 and found the two solutions. Finally, we rounded the irrational solutions to the nearest tenth.

Answer

The solutions to the equation $x^2 + 7x + 8 = 0$ are $x = -5.6$ and $x = -1.4$.

Discussion

The quadratic formula is a powerful tool that can be used to find the solutions to any quadratic equation in the form of $ax^2 + bx + c = 0$. The formula consists of two parts: the first part is the negative of the coefficient of the linear term ($-b$), and the second part is the square root of the discriminant ($\sqrt{b^2 - 4ac}$). The quadratic formula can be used to solve quadratic equations that cannot be factored or solved using other methods.

Example Problems

1. Solve the equation $x^2 + 5x + 6 = 0$ using the quadratic formula.
2. Solve the equation $x^2 - 3x - 4 = 0$ using the quadratic formula.
3. Solve the equation $x^2 + 2x + 1 = 0$ using the quadratic formula.

Solutions

1. The solutions to the equation $x^2 + 5x + 6 = 0$ are $x = -2$ and $x = -3$.
2. The solutions to the equation $x^2 - 3x - 4 = 0$ are $x = 4$ and $x = -1$.
3. The solutions to the equation $x^2 + 2x + 1 = 0$ are $x = -1$ and $x = -1$.

Conclusion

$$$$$$$$

Frequently Asked Questions

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that can be used to find the solutions to any quadratic equation in the form of $ax^2 + bx + c = 0$. 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 equation. Then, you plug these values into the formula and simplify the expression. Finally, you find the two solutions by plugging in the positive and negative values of the square root.

Q: What is the discriminant?

A: The discriminant is the expression inside the square root in the quadratic formula. It is given by $b^2 - 4ac$. If the discriminant is positive, the equation has two real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has no real solutions.

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

A: Yes, you can use the quadratic formula to solve any quadratic equation in the form of $ax^2 + bx + c = 0$. However, if the equation cannot be factored or solved using other methods, the quadratic formula may be the only way to find the solutions.

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

A: To round irrational solutions to the nearest tenth, you need to look at the hundredth place digit. If the digit is 5 or greater, you round up. If the digit is 4 or less, you round down.

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 correctly
• Not finding the two solutions correctly
• Not rounding irrational solutions to the nearest tenth correctly

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. However, the solutions will be in the form of complex numbers, which can be written in the form of $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit.

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

A: To use the quadratic formula to solve quadratic equations with complex solutions, you need to follow the same steps as before. However, when you find the two solutions, you will get complex numbers. You can then simplify the complex numbers to get the final solutions.

Conclusion

In this article, we answered some frequently asked questions about the quadratic formula. We covered topics such as how to use the quadratic formula, what the discriminant is, and how to round irrational solutions to the nearest tenth. We also discussed some common mistakes to avoid when using the quadratic formula and how to use the quadratic formula to solve quadratic equations with complex solutions.