What Is The Solution Of X + 12 = X \sqrt{x+12}=x X + 12 ​ = X ?A. X = − 3 X=-3 X = − 3 B. X = 4 X=4 X = 4 C. X = − 3 Or X = 4 X=-3 \text{ Or } X=4 X = − 3 Or X = 4 D. No Solution

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Introduction

Solving equations involving square roots can be a challenging task, especially when the variable is inside the square root. In this article, we will explore the solution to the equation $\sqrt{x+12}=x$. This equation involves a square root and a variable, making it a great example of how to solve equations with radicals.

Understanding the Equation

The given equation is $\sqrt{x+12}=x$. To solve this equation, we need to isolate the variable $x$. The first step is to square both sides of the equation to eliminate the square root. Squaring both sides gives us:

$$x+12=x^2$$

Rearranging the Equation

Now that we have squared both sides of the equation, we can rearrange the terms to get a quadratic equation in standard form. Subtracting $x$ from both sides gives us:

$$12=x^2-x$$

Factoring the Quadratic Equation

The quadratic equation $12=x^2-x$ can be factored as:

$$12=x(x-1)$$

Solving for $x$

To solve for $x$, we can set each factor equal to zero and solve for $x$. Setting the first factor equal to zero gives us:

$$x=0$$

However, this is not a valid solution because it would make the original equation undefined. Setting the second factor equal to zero gives us:

$$x-1=0$$

Solving for $x$ gives us:

$$x=1$$

Checking the Solutions

Now that we have found two possible solutions, $x=0$ and $x=1$, we need to check if they are valid. Plugging $x=0$ into the original equation gives us:

$$\sqrt{0+12}=\sqrt{12}$$

However, $\sqrt{12}$ is not equal to $0$, so $x=0$ is not a valid solution. Plugging $x=1$ into the original equation gives us:

$$\sqrt{1+12}=\sqrt{13}$$

However, $\sqrt{13}$ is not equal to $1$, so $x=1$ is not a valid solution either.

Conclusion

After checking the solutions, we find that neither $x=0$ nor $x=1$ is a valid solution to the equation $\sqrt{x+12}=x$. This means that the equation has no solution.

Final Answer

The final answer is D. No solution.

Discussion

The equation $\sqrt{x+12}=x$ is a classic example of how to solve equations with radicals. However, in this case, the equation has no solution. This is because the quadratic equation $12=x^2-x$ has no real solutions, and therefore, the original equation has no solution.

Related Topics

• Solving equations with radicals
• Quadratic equations
• No solution to an equation

References

• [1] "Solving Equations with Radicals" by Math Open Reference
• [2] "Quadratic Equations" by Khan Academy
• [3] "No Solution to an Equation" by Purplemath
  

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Introduction

In our previous article, we explored the solution to the equation $\sqrt{x+12}=x$. We found that the equation has no solution. In this article, we will answer some frequently asked questions related to solving the equation $\sqrt{x+12}=x$.

Q: What is the equation $\sqrt{x+12}=x$?

A: The equation $\sqrt{x+12}=x$ is a quadratic equation that involves a square root. It is a classic example of how to solve equations with radicals.

Q: Why is the equation $\sqrt{x+12}=x$ difficult to solve?

A: The equation $\sqrt{x+12}=x$ is difficult to solve because it involves a square root and a variable. When we square both sides of the equation, we get a quadratic equation that has no real solutions.

Q: What is the quadratic equation that results from squaring both sides of the equation $\sqrt{x+12}=x$?

A: The quadratic equation that results from squaring both sides of the equation $\sqrt{x+12}=x$ is $12=x^2-x$.

Q: Can we factor the quadratic equation $12=x^2-x$?

A: Yes, we can factor the quadratic equation $12=x^2-x$ as $12=x(x-1)$.

Q: What are the possible solutions to the equation $12=x(x-1)$?

A: The possible solutions to the equation $12=x(x-1)$ are $x=0$ and $x=1$.

Q: Are the solutions $x=0$ and $x=1$ valid?

A: No, the solutions $x=0$ and $x=1$ are not valid because they do not satisfy the original equation $\sqrt{x+12}=x$.

Q: Why is the equation $\sqrt{x+12}=x$ important?

A: The equation $\sqrt{x+12}=x$ is important because it is a classic example of how to solve equations with radicals. It also illustrates the concept of no solution to an equation.

Q: What are some related topics to the equation $\sqrt{x+12}=x$?

A: Some related topics to the equation $\sqrt{x+12}=x$ include solving equations with radicals, quadratic equations, and no solution to an equation.

Q: Where can I learn more about solving equations with radicals?

A: You can learn more about solving equations with radicals by visiting websites such as Math Open Reference or Khan Academy.

Q: What is the final answer to the equation $\sqrt{x+12}=x$?

A: The final answer to the equation $\sqrt{x+12}=x$ is D. No solution.

Conclusion

In this article, we answered some frequently asked questions related to solving the equation $\sqrt{x+12}=x$. We found that the equation has no solution and that it is a classic example of how to solve equations with radicals. We also discussed some related topics and provided resources for further learning.

Final Answer

The final answer is D. No solution.

Discussion

The equation $\sqrt{x+12}=x$ is a challenging equation that involves a square root and a variable. However, with the right techniques and resources, we can solve it and learn more about solving equations with radicals.

Related Topics

• Solving equations with radicals
• Quadratic equations
• No solution to an equation

References

• [1] "Solving Equations with Radicals" by Math Open Reference
• [2] "Quadratic Equations" by Khan Academy
• [3] "No Solution to an Equation" by Purplemath