Extraneous solutions are those solutions encountered when solving an equation or system of equations that at first glance appear reasonable, but do not actually satisfy the original conditions of the problem. Extraneous solutions can occur with any type of equation--including differential equations--but most often occur when a problem involves applying the square, quartic, or any other even-numbered power to both sides of an equation. Extraneous solutions also sometimes occur when the problem involves a radical term (that is, a term with a non-integer exponent) or trigonometric function, or when the restrictions on the domains of terms in the equation(s) are not well-considered. Extraneous solutions are also quite common when a mathematical model is applied to a real-world event, scientific experiment, or engineering problem, as models generally apply only to a well-defined domain, such as the time between the start of a race and the time...