What Is The Solution Of − 4 X = 100 \sqrt{-4x} = 100 − 4 X ​ = 100 ?A. X = − 2500 X = -2500 X = − 2500 B. X = − 50 X = -50 X = − 50 C. X = − 2.5 X = -2.5 X = − 2.5 D. No Solution

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What is the Solution of −4x=100\sqrt{-4x} = 100?

In this article, we will explore the solution of the equation −4x=100\sqrt{-4x} = 100. This equation involves a square root and a variable xx, and we will use algebraic techniques to solve for xx. We will also discuss the validity of the solutions and the implications of the equation.

The given equation is −4x=100\sqrt{-4x} = 100. To solve for xx, we need to isolate the variable xx on one side of the equation. However, the presence of the square root makes it challenging to solve the equation directly.

Squaring Both Sides

One common technique to eliminate the square root is to square both sides of the equation. This is a valid operation, but it requires caution to ensure that the resulting equation is not invalid.

\sqrt{-4x} = 100

Squaring both sides of the equation, we get:

(-4x) = 100^2

Simplifying the right-hand side, we get:

-4x = 10000

Solving for xx

Now that we have a linear equation, we can solve for xx by dividing both sides of the equation by −4-4.

-4x = 10000

Dividing both sides by −4-4, we get:

x = -\frac{10000}{4}

Simplifying the expression, we get:

x = -2500

In this article, we solved the equation −4x=100\sqrt{-4x} = 100 by squaring both sides of the equation and then solving for xx. The solution to the equation is x=−2500x = -2500. This solution is valid, and it satisfies the original equation.

The equation −4x=100\sqrt{-4x} = 100 involves a square root and a variable xx. The presence of the square root makes it challenging to solve the equation directly. However, by squaring both sides of the equation, we can eliminate the square root and solve for xx.

The solution to the equation −4x=100\sqrt{-4x} = 100 has implications for the value of xx. The solution x=−2500x = -2500 indicates that the value of xx must be negative to satisfy the equation.

The solution x=−2500x = -2500 is compared with the options provided:

  • A. x=−2500x = -2500
  • B. x=−50x = -50
  • C. x=−2.5x = -2.5
  • D. No solution

The solution x=−2500x = -2500 matches option A.

In conclusion, the solution to the equation −4x=100\sqrt{-4x} = 100 is x=−2500x = -2500. This solution is valid, and it satisfies the original equation. The presence of the square root makes it challenging to solve the equation directly, but by squaring both sides of the equation, we can eliminate the square root and solve for xx.
Frequently Asked Questions (FAQs) about the Solution of −4x=100\sqrt{-4x} = 100

In our previous article, we explored the solution of the equation −4x=100\sqrt{-4x} = 100. We used algebraic techniques to solve for xx and found that the solution is x=−2500x = -2500. In this article, we will address some frequently asked questions (FAQs) about the solution of the equation.

Q: What is the significance of the negative sign in the equation?

A: The negative sign in the equation −4x=100\sqrt{-4x} = 100 indicates that the value of xx must be negative to satisfy the equation. This is because the square root of a negative number is an imaginary number, and the product of two imaginary numbers is a real number.

Q: Why did we square both sides of the equation?

A: We squared both sides of the equation to eliminate the square root. This is a common technique used to solve equations involving square roots. However, it requires caution to ensure that the resulting equation is not invalid.

Q: Is the solution x=−2500x = -2500 unique?

A: Yes, the solution x=−2500x = -2500 is unique. This is because the equation −4x=100\sqrt{-4x} = 100 has only one solution, and that solution is x=−2500x = -2500.

Q: What happens if we try to solve the equation −4x=100\sqrt{-4x} = 100 using other methods?

A: If we try to solve the equation −4x=100\sqrt{-4x} = 100 using other methods, we will not get a valid solution. This is because the equation involves a square root and a variable xx, and the presence of the square root makes it challenging to solve the equation directly.

Q: Can we use the solution x=−2500x = -2500 to solve other equations involving square roots?

A: Yes, we can use the solution x=−2500x = -2500 to solve other equations involving square roots. However, we need to be cautious and ensure that the resulting equation is valid.

Q: What is the relationship between the solution x=−2500x = -2500 and the options provided?

A: The solution x=−2500x = -2500 matches option A. This is because the solution x=−2500x = -2500 is the correct answer to the equation −4x=100\sqrt{-4x} = 100.

Q: Can we use the solution x=−2500x = -2500 to solve equations involving other variables?

A: Yes, we can use the solution x=−2500x = -2500 to solve equations involving other variables. However, we need to be cautious and ensure that the resulting equation is valid.

In conclusion, the solution to the equation −4x=100\sqrt{-4x} = 100 is x=−2500x = -2500. This solution is unique and satisfies the original equation. We have addressed some frequently asked questions (FAQs) about the solution of the equation and provided answers to help clarify any doubts.

For more information about solving equations involving square roots, please refer to the following resources:

The information provided in this article is for educational purposes only. It is not intended to be used as a substitute for professional advice or guidance. If you have any questions or concerns about solving equations involving square roots, please consult a qualified mathematician or educator.