What's x that makes x² + 2x = 24? Unlock the Equation's Secret!

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Are you ready to embark on a journey of mathematical discovery? Brace yourself as we unravel the mystery behind the equation X^2 + 2x = 24. This seemingly complex expression holds the key to unlocking a world where numbers come alive and equations speak volumes. By understanding the values of x that make this equation true, we will delve into the realm of solutions and unveil a hidden treasure trove of mathematical possibilities. So, fasten your seatbelt and get ready to explore the fascinating world of X^2 + 2x = 24!


Introduction

In this article, we will explore the values of x for which the equation x^2 + 2x = 24 holds true. By solving this quadratic equation, we can determine the specific values of x that satisfy the equation. Let's dive into the process and find out the possible solutions to this equation.

Simplifying the Equation

To begin, let's simplify the given equation x^2 + 2x = 24. By subtracting 24 from both sides, we obtain x^2 + 2x - 24 = 0. This form of the equation allows us to easily apply factoring or the quadratic formula to find the solutions.

Factoring the Quadratic Equation

To factor the quadratic equation x^2 + 2x - 24 = 0, we need to find two numbers whose product is -24 and whose sum is 2. After considering the factors of -24, we discover that the numbers are 6 and -4. Now, we can rewrite the equation as (x + 6)(x - 4) = 0.

Using the Zero Product Property

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. Applying this property to our equation (x + 6)(x - 4) = 0, we can set each factor equal to zero and solve for x.

Solving for x + 6 = 0

By setting x + 6 = 0, we subtract 6 from both sides, resulting in x = -6. Hence, -6 is one of the values for x that satisfies the given equation.

Solving for x - 4 = 0

Similarly, by setting x - 4 = 0, we add 4 to both sides of the equation and find x = 4. Therefore, 4 is another value for x that makes the original equation true.

Conclusion

After solving the quadratic equation x^2 + 2x = 24, we found that the values of x which satisfy the equation are -6 and 4. By substituting these values back into the equation, we can verify their accuracy. It is important to note that these are the only two solutions for this particular equation. We hope this article helped clarify the values of x that make this quadratic equation true.

Further Exploration

If you found this topic interesting, there is much more to explore in the realm of quadratic equations. You can delve deeper into factoring, quadratic formulas, or even explore complex numbers. Understanding these concepts will strengthen your mathematical foundation and help you solve more complex problems in the future.

References

1. Quadratic Equations: Factoring and the Zero Product Property. Retrieved from [insert link]

2. The Zero Product Property. Retrieved from [insert link]

3. Quadratic Equations. Retrieved from [insert link]


Introduction:

Solving the quadratic equation X^2 + 2x = 24 allows us to find the values of x that satisfy the equation. By understanding the steps involved in solving this equation, we can determine the valid solutions.

Setting up the equation:

To begin, we must determine the quadratic equation by combining like terms and rearranging them to equal zero. In this case, the equation is X^2 + 2x - 24 = 0.

Factoring the equation:

One approach to easily determine the values of x that make the equation true is by factoring the quadratic equation. By factoring X^2 + 2x - 24, we obtain (X + 6)(X - 4) = 0.

Zero-factor property:

The zero-factor property states that if a product of two factors equals zero, then at least one of the factors must be zero. Applying this property, we can find the values of x that satisfy the equation by equating each factor to zero: X + 6 = 0 or X - 4 = 0.

Solving for X+6:

To solve for X in the first equation, we isolate X by subtracting 6 from both sides: X = -6.

Solving for X-4:

Similarly, to solve for X in the second equation, we isolate X by adding 4 to both sides: X = 4.

Determining the valid values of x:

From our calculations, we have found that the equation X^2 + 2x = 24 is true when x equals -6 or 4. These are the values of x that satisfy the given equation.

Verifying the solutions:

To ensure the correctness of our solutions, we can plug the values of -6 and 4 into the original equation and check if both values make the equation true. Substituting -6 into the equation, we have (-6)^2 + 2(-6) = 24. Simplifying, we get 36 - 12 = 24, which is true. Similarly, substituting 4 into the equation, we have (4)^2 + 2(4) = 24. Again, simplifying, we get 16 + 8 = 24, which is also true.

Confirming validity:

Through the verification process, we observe that both -6 and 4 indeed satisfy the equation X^2 + 2x = 24. This confirms their validity as solutions for the given quadratic equation.

Conclusion:

In conclusion, the equation X^2 + 2x = 24 holds true for the values of x equal to -6 and 4. By following the steps of setting up the equation, factoring it, applying the zero-factor property, and solving for x, we have obtained a comprehensive solution to the quadratic equation. The validity of the solutions has been confirmed through verification, providing confidence in the accuracy of our findings.

When solving the equation x^2 + 2x = 24, we need to find the values of x that make the equation true. Let's break down the steps to determine these values:

  1. Start by subtracting 24 from both sides of the equation: x^2 + 2x - 24 = 0.
  2. We now have a quadratic equation in standard form, which can be factored or solved using the quadratic formula.
  3. In order for the equation to be true, the expression on the left-hand side must equal zero. So, we need to find the values of x that make the equation equal to zero.
  4. Let's factor the quadratic equation: (x - 4)(x + 6) = 0.
  5. Now, we can set each factor equal to zero and solve for x:
  • x - 4 = 0: Adding 4 to both sides gives us x = 4.
  • x + 6 = 0: Subtracting 6 from both sides gives us x = -6.

Therefore, the values of x that satisfy the equation x^2 + 2x = 24 are x = 4 and x = -6.


Thank you for visiting our blog post on the topic of For What Values of x is x^2 + 2x = 24 True? We hope that you have found this article informative and helpful in understanding how to solve quadratic equations and find the values of x that satisfy the given equation. In this closing message, we would like to summarize the key points discussed in the article and provide some final thoughts on the topic.

In the first paragraph of our article, we introduced the equation x^2 + 2x = 24 and explained the importance of finding the values of x that make this equation true. We then proceeded to guide you through the process of solving the quadratic equation by factoring. By factoring the equation, we were able to rewrite it in the form (x + a)(x + b) = 0, where a and b are constants. This allowed us to identify the roots of the equation, which are the values of x that satisfy the equation.

In the second paragraph, we provided a step-by-step explanation of how to factor the quadratic equation x^2 + 2x = 24. We showed you how to rearrange the equation to bring all terms to one side and then factor out the common factor. By setting each factor equal to zero, we were able to find the two possible values of x that satisfy the equation. These values are x = -6 and x = 4. We also explained that these values represent the x-intercepts of the graph of the quadratic equation.

In the final paragraph, we emphasized the importance of checking our solutions to ensure that they indeed make the equation true. We highlighted that substituting the values of x back into the original equation and simplifying both sides will confirm if the solutions are valid. In this case, substituting x = -6 and x = 4 into the equation x^2 + 2x = 24 indeed yields a true statement. We concluded the article by urging you to practice solving similar quadratic equations to further enhance your understanding and mastery of this topic.

We hope that this blog post has provided you with a clear explanation of how to find the values of x that make the equation x^2 + 2x = 24 true. If you have any further questions or if there are any other topics you would like us to cover, please feel free to leave a comment or reach out to us. Thank you once again for visiting our blog, and we hope to see you again soon!


For What Values Of X Is X^2 + 2x = 24 True?

1. What is the equation we are trying to solve?

The equation we are trying to solve is X^2 + 2x = 24.

2. How can we find the values of X that satisfy the equation?

To find the values of X that satisfy the equation, we need to manipulate the equation and solve for X.

Using the quadratic formula:

  1. First, rewrite the equation in the form ax^2 + bx + c = 0. In this case, we have x^2 + 2x - 24 = 0.
  2. Identify the values of a, b, and c. Here, a = 1, b = 2, and c = -24.
  3. Plug the values of a, b, and c into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
  4. Simplify the equation using the values of a, b, and c: x = (-2 ± √(2^2 - 4*1*(-24))) / (2*1).
  5. Calculate the discriminant (b^2 - 4ac) to determine the number of solutions. If the discriminant is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are no real solutions.
  6. Compute the values of X by evaluating the quadratic formula with the calculated values. These will give the possible values of X that satisfy the equation.

Factoring the equation:

  1. Rewrite the equation in the form ax^2 + bx + c = 0. Here, we have x^2 + 2x - 24 = 0.
  2. Factor the quadratic equation into two binomials: (x + 6)(x - 4) = 0.
  3. Set each binomial equal to zero and solve for X:
    • x + 6 = 0 → x = -6
    • x - 4 = 0 → x = 4
  4. The values of X that satisfy the equation are -6 and 4.

3. What are the solutions to the equation?

The solutions to the equation X^2 + 2x = 24 are x = -6 and x = 4.