Final answer:
The given equation (2x)^2 = 4.0 (1 - x)^2 leads to two possible solutions when simplified; solving for x yields x = 1/2, while the second simplification does not provide a specific solution. To solve problems, identify knowns and unknowns and use equations that contain only one unknown.
Step-by-step explanation:
The original math problem appears to be an expression rather than an equation: x + (4)/(x^2). However, the later parts of the question refer to solving an equation. The given equation (2x)² = 4.0 (1 − x)² can be simplified by taking the square root of both sides, which yields (2x) = ± 2(1 - x). This results in two possible equations: 2x = 2 - 2x and 2x = -2 + 2x. Solving the first equation for x gives x = 1/2, and the second equation simplifies to 0 = 0, which is true for all x and does not give a specific solution.
When analyzing data and finding solutions, being approximate with numbers allows for easier mental calculation. To solve a problem involving an equation, one should identify knowns and unknowns, find an equation that contains only one unknown, and solve for it. If there is more than one unknown, additional equations are needed. In some cases, multiple equations may be required to solve for a single needed unknown, and it's important to have a solid grasp of the necessary physical principles.