Final answer:
The question deals with various algebraic techniques used to solve quadratic equations, such as expanding expressions, using the quadratic formula, and completing the square. These methods are essential for solving for the variable 'x' in equations of the form 'ax² + bx + c = 0'.
Step-by-step explanation:
The question appears to concern different algebraic techniques for solving quadratic equations and other related expressions. At its core, the steps shared direct students on how to manipulate and solve quadratic expressions.
The reference to 'Example 16.7.3' seems to indicate a specific example from a text, likely dealing with solving quadratic equations or simplifying algebraic expressions. The subsequent instructions, such as 'expanding the expression', 'multiplying both sides by the denominator', and 'rearranging into a quadratic equation that equals 0' are the steps typically followed in algebra to solve for variables.
The use of the quadratic formula, completing the square, and factoring expressions are standard methods to solve quadratic equations. Each methodology provides a systematic way to arrive at the roots of the equation, which are the possible values of 'x' that satisfy the equation 'ax² + bx + c = 0'.