What Are The Solutions To The Quadratic Equation Below? X 2 + 34 X − 72 = 0 X^2 + 34x - 72 = 0 X 2 + 34 X − 72 = 0 A. X = − 36 X = -36 X = − 36 And X = 2 X = 2 X = 2 B. X = 36 X = 36 X = 36 And X = − 2 X = -2 X = − 2 C. X = − 24 X = -24 X = − 24 And X = − 3 X = -3 X = − 3 D. X = 24 X = 24 X = 24 And $x =

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Introduction

Quadratic equations are a fundamental concept in mathematics, and they have numerous applications in various fields, including physics, engineering, and economics. A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. In this article, we will focus on solving the quadratic equation $x^2 + 34x - 72 = 0$.

The Quadratic Formula

The quadratic formula is a powerful tool for solving quadratic equations. It is given by:

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

where $a$, $b$, and $c$ are the coefficients of the quadratic equation. In our case, $a = 1$, $b = 34$, and $c = -72$. Plugging these values into the quadratic formula, we get:

$$x = \frac{-34 \pm \sqrt{34^2 - 4(1)(-72)}}{2(1)}$$

Simplifying the Quadratic Formula

Now, let's simplify the quadratic formula by evaluating the expression inside the square root:

$$x = \frac{-34 \pm \sqrt{1156 + 288}}{2}$$

$$x = \frac{-34 \pm \sqrt{1444}}{2}$$

$$x = \frac{-34 \pm 38}{2}$$

Solving for x

Now, we have two possible solutions for $x$:

$$x = \frac{-34 + 38}{2} = \frac{4}{2} = 2$$

$$x = \frac{-34 - 38}{2} = \frac{-72}{2} = -36$$

Checking the Solutions

To verify that these solutions are correct, we can plug them back into the original equation:

$$x^2 + 34x - 72 = 0$$

For $x = 2$:

$$(2)^2 + 34(2) - 72 = 4 + 68 - 72 = 0$$

For $x = -36$:

$$(-36)^2 + 34(-36) - 72 = 1296 - 1224 - 72 = 0$$

Conclusion

In conclusion, the solutions to the quadratic equation $x^2 + 34x - 72 = 0$ are $x = 2$ and $x = -36$. These solutions can be verified by plugging them back into the original equation.

Final Answer

The final answer is:

A. $x = -36$ and $x = 2$

This is the correct solution to the quadratic equation $x^2 + 34x - 72 = 0$.

Introduction

Quadratic equations are a fundamental concept in mathematics, and they have numerous applications in various fields, including physics, engineering, and economics. In our previous article, we solved the quadratic equation $x^2 + 34x - 72 = 0$ using the quadratic formula. In this article, we will provide a Q&A guide to help you understand the solutions to quadratic equations.

Q: What is a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: What is the quadratic formula?

A: The quadratic formula is a powerful tool for solving quadratic equations. It is given by:

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

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

Q: How do I use the quadratic formula to solve a quadratic equation?

A: To use the quadratic formula, you need to plug in the values of $a$, $b$, and $c$ into the formula. Then, simplify the expression inside the square root and solve for $x$.

Q: What are the possible solutions to a quadratic equation?

A: The quadratic formula gives two possible solutions to a quadratic equation:

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

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

Q: How do I check if the solutions are correct?

A: To verify that the solutions are correct, you can plug them back into the original equation. If the equation is true, then the solution is correct.

Q: What are some common mistakes to avoid when solving quadratic equations?

A: Some common mistakes to avoid when solving quadratic equations include:

• Not simplifying the expression inside the square root
• Not plugging in the correct values of $a$, $b$, and $c$ into the quadratic formula
• Not checking if the solutions are correct

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

A: Yes, the quadratic formula can be used to solve all types of quadratic equations, including those with complex solutions.

Q: What are some real-world applications of quadratic equations?

A: Quadratic equations have numerous applications in various fields, including physics, engineering, and economics. Some examples include:

• Projectile motion
• Optimization problems
• Electrical circuits
• Computer graphics

Q: Can I use technology to solve quadratic equations?

A: Yes, there are many online tools and calculators that can be used to solve quadratic equations. However, it's always a good idea to understand the underlying math and be able to solve the equation by hand.

Conclusion

In conclusion, quadratic equations are a fundamental concept in mathematics, and they have numerous applications in various fields. By understanding the quadratic formula and how to use it to solve quadratic equations, you can tackle a wide range of problems and applications.

Final Tips

• Always simplify the expression inside the square root
• Plug in the correct values of $a$, $b$, and $c$ into the quadratic formula
• Check if the solutions are correct
• Use technology to check your work, but always understand the underlying math.