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:
- Identify the given equation which is assumed to represent the equilibrium state: (x)(x) = (0.0150x)(0.0150 - x).
- As noted in the question, the left side of the equation is a perfect square, thus it simplifies to x².
- 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).
- Solve for x by taking the square root of both sides, leading us to x = 0.0150 - x, which implies 2x = 0.0150.
- 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.