Final answer:
The student's question involves simplifying a rational algebraic expression and solving quadratic equations where specific methods like factoring or the quadratic formula are used to find the values of x.
Step-by-step explanation:
The given expression, ((x+27)(x-2))/((x+12)(x-7)), cannot be simplified by cancellation, and evaluating it for the given values of x, such as x = 0.0216 or x = -0.0224, allows us to find specific numerical values for the entire expression. When raising expressions to a power, everything inside the parentheses is affected, as seen in the example (27x3)(4x2) = 2.1 × 10-33. If solving quadratic equations similar to x2 + 0.0211x - 0.0211 = 0, the quadratic formula or factoring can be utilized. Special attention should be paid to the format of the equation, ax2 + bx + c = 0, to correctly apply the quadratic formula.1