Final answer:
To solve the given equation, isolate square roots, square both sides and then use standard algebraic techniques such as the quadratic formula to find the solution.
Step-by-step explanation:
The question presented requires the solution of a mathematical equation that includes variables, radicals, and quadratic terms. The equation resembles something that could be derived from physics concepts, as there are expressions reminiscent of kinematic equations, but the context is purely mathematical.
First, let's assess the given snippets and see if they provide a coherent approach to solving the equation - -x + √(1 - x²) = √2(2x² - 1). It appears that the information is fragmented and taken from different contexts. For instance, there is a partial mention of completing the square and using the quadratic formula, but without an actual coherent process to solve the original equation.
Thus, the recommended approach is to first isolate the square root terms, square both sides to eliminate the roots, and then move all terms to one side of the equation to form a standard quadratic equation ax² + bx + c = 0. The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), or factoring can then be applied to find the solution(s).