Problem 128 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I solve an equation that is quadratic in form, it's important to write down the substitution that I am making.

Step-by-Step Solution

Answer

The statement makes sense because writing down the substitution when solving a quadratic equation provides a clear, followable solution process and allows for verification of your answer.

Step 1: Understand Quadratic Equation

A quadratic equation is an equation of the form \(ax^2+bx+c=0\), where \(a, b,\) and \(c\) are constants. Solving this type of equation often involves factoring or the application of the quadratic formula.

Step 2: Understand Substitution

Sometimes, to simplify the process of solving a quadratic equation, a substitution is made. A variable is replaced with another variable or expression to make the equation easier to solve.

Step 3: Making sense of the Statement

Given these facts, the statement makes sense. When performing a substitution while solving a quadratic equation, writing down what substitution was made is crucial. Not only does this practice allow for verification of your answer, but it also allows others to understand your process.