Final answer:
The statement 'x = 4' needs context to be considered an algebraic proof. An algebraic proof involves deriving the value of x from a given equation through methods such as taking square roots, rearranging, or using the quadratic formula.
Step-by-step explanation:
When the equation (2x)² = 4.0 (1 − x)² is given, we are dealing with an algebraic proof where the objective is to find the value of x. To uncover the value of x, we can take the square root of both sides, considering that both the fraction and the 4.0 on the right side are perfect squares. This simplifies to (2x)(1 − x). By rearranging and solving, we can determine the value of x. If we substitute x with 4, we can check if the original equation holds true. However, in this case, if we put x = 4 into our equation, we find that it does not satisfy the equation, indicating that x = 4 is not a solution to the given equation.
Regarding the algebraic equation x² +0.0211x -0.0211 = 0, one could use the quadratic formula or complete the square to find the solutions for x. This process involves identifying ax² + bx + c in the equation and using algebraic methods to solve for the variable x.
In summary, the original statement x = 4 does not stand as a valid algebraic proof without the proper context or equation showing that x indeed equals 4.