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Find the value of x. Give reasons to justify your solution. D ∈ AC

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Final answer:

To find the value of x, we equate the squares on both sides of the equilibrium equation, solve for x using algebraic manipulations, and conclude that x = 0.0075.

Step-by-step explanation:

To find the value of x, we have to solve the equation given. The provided equation suggests a chemical equilibrium scenario where products and reactants are in a dynamic balance represented by K, the equilibrium constant. Let's break down the solution step by step:

  1. Identify the given equation which is assumed to represent the equilibrium state: (x)(x) = (0.0150x)(0.0150 - x).
  2. As noted in the question, the left side of the equation is a perfect square, thus it simplifies to x².
  3. Rewrite the equation as x² = (0.0150 - x)². This indicates that x must be a value that when squared, equals the square of (0.0150 - x).
  4. Solve for x by taking the square root of both sides, leading us to x = 0.0150 - x, which implies 2x = 0.0150.
  5. Dividing both sides by 2 gives us x = 0.0075.

The justification for the solution involves understanding the properties of perfect squares and basic algebraic manipulation to isolate the variable x.

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