Final answer:
The equation (2x)² = 4.0 (1 − x)² simplifies to (2x)(1 − x), and by using algebraic manipulation and the concept that x² = √x, we solve for x and express it as a simplified radical.
Step-by-step explanation:
To find the measure of side x, we are given the equation (2x)² = 4.0 (1 − x)² which simplifies to (2x)(1 − x). Recognizing this as a perfect square allows us to solve for x by taking the square root of both sides. Referring to the concept that x² = √x, we can solve for x by isolating the variable after simplification.We can see the equation involves simplification of a perfect square and application of basic algebraic manipulation. The equation hints at familiar algebraic principles such as exponent rules and square roots which are applicable to solving for x.
Considering the given options and the procedure of simplification and solving, we arrive at the correct choice for the measure of side x which is represented by a simplified radical.To find the measure of side x, we can start by squaring both sides of the given equation:(2x)² = 4.0 (1 − x)²This simplifies to:4x² = 4(1 − x)²Next, we can take the square root of both sides:√(4x²) = √(4(1 − x)²)This further simplifies to:2|x| = 2|1 − x|Now, we can rewrite the absolute value equation as two separate equations:2x = 2(1 − x) or 2x = -(2(1 − x))Solving the first equation: