There are three cases with any quadratic equation: one real solution, two real solutions, or no real solutions (complex solutions). Once you have the values of \(a\), \(b\), and \(c\), the final step is to substitute them into the formula and simplify. To keep it simple, just remember to carry the sign into the formula. Why are \(b\) and \(c\) negative? The formula is based off the form \(ax^2+bx+c=0\) where all the numerical values are being added and we can rewrite \(x^2-x-6=0\) as \(x^2 + (-x) + (-6) = 0\).
Now that we have it in this form, we can see that: As you can see above, the formula is based on the idea that we have 0 on one side. Exampleīefore we do anything else, we need to make sure that all the terms are on one side of the equation. Let’s take a look at a couple of examples. If your equation is not in that form, you will need to take care of that as a first step. A quadratic equation is any equation that can be written as ax2+bx+c0, for some numbers a, b, and c, where a is nonzero.
Applying this formula is really just about determining the values of \(a\), \(b\), and \(c\) and then simplifying the results.īut, it is important to note the form of the equation given above. Looking at the formula below, you can see that \(a\), \(b\), and \(c\) are the numbers straight from your equation. Examples of applying the quadratic formula
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