Final answer:
To address the question, one would simplify the denominator into a perfect square, recognize any perfect squares within the equation, use the quadratic formula if necessary, and consider both positive and negative square roots when solving for the variable x.
Step-by-step explanation:
The question involves simplifying a complex algebraic expression and potentially solving it for the variable x.
To tackle this algebraic expression, one can begin by simplifying the denominator to get a perfect square and then attempt to perform operations to isolate the variable. When you encounter a perfect square such as (2x)² or 4.0 (1 − x)², you can take the square root of both sides which will simplify the equation substantially.
Rearranging and solving for x may require the use of quadratic formula, which is used for equations of the form ax² + bx + c = 0. In some instances, recognizing a perfect square on one side of the equation can simplify the solving process.
Furthermore, upon solving for x, the equation may yield two solutions, corresponding to the positive and negative square roots, so both possibilities should be considered.