Classify and Solve Quadratic Equations (Part 2)

As mentioned in the previous lesson, trinomial quadratics containing a first degree and second degree term, along with a constant, are called complete quadratics. Just like pure and incomplete quadratics, solving complete quadratics is as simple as setting y = 0 and solving for x.

  • Remember, to solve an equation means to find the values of the variable that make the statement true. This is also called finding the roots of the equation.

Solving complete quadratics is entirely depended on knowing how to factor, and this is why you learned it earlier. If you skipped those lessons, you need to know how to factor trinomials. The techniques you’ve learned already included factoring by trial-and-error and decomposition (linked). Let’s start with two examples where you first factor by trial-and-error. Recall that this technique only works when the coefficient in front of the x² term is 1:

The next video shows how to first factor by decomposition, then solve for the x’s, and finally graph the information. (Note: The question mentions “the quadratic formula“, but it isn’t used). The graphing part somewhat foreshadows what we’ll be doing in our next lesson, so if you’d like to skip that part for later, feel free to do so as it’ll be covered in greater detail soon.