What is the solution of $\sqrt{-4 x}=100$?
A. $x=-2500$
B. $x=-50$
C. $x=-2.5$
D. no solution
Answer (2)
The solution to the equation − 4 x = 100 is x = − 2500 , confirmed by substituting this value back into the equation. Therefore, the correct choice is option A: -2500.
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Square both sides of the equation: ( − 4 x ) 2 = 10 0 2 .
Simplify the equation: − 4 x = 10000 .
Divide both sides by -4: x = − 4 10000 .
Calculate the value of x : x = − 2500 , so the final answer is − 2500 .
Explanation
Understanding the Problem We are given the equation − 4 x = 100 . Our goal is to find the value of x that satisfies this equation.
Squaring Both Sides To solve for x , we first need to eliminate the square root. We can do this by squaring both sides of the equation: ( − 4 x ) 2 = 10 0 2
Simplifying the Equation Simplifying the equation, we get: − 4 x = 10000
Isolating x Now, we need to isolate x . We can do this by dividing both sides of the equation by -4: x = − 4 10000
Calculating x Calculating the value of x , we find: x = − 2500
Checking the Solution To make sure our solution is correct, we should check it by substituting x = − 2500 back into the original equation: − 4 ( − 2500 ) = 10000 = 100 Since the solution satisfies the original equation, x = − 2500 is indeed the solution.
Final Answer Therefore, the solution to the equation − 4 x = 100 is x = − 2500 .
Examples
Imagine you're designing a safety system where a sensor measures a value related to a critical variable, x . The system is designed to trigger an alarm if − 4 x reaches 100. Solving the equation − 4 x = 100 helps you determine the exact value of x at which the alarm should be triggered, ensuring the system responds correctly to potential hazards. This kind of problem arises in various engineering and scientific contexts where understanding the relationship between variables and their square roots is crucial for system design and safety.
