A quadratic equation is a polynomial equation in a single variable where the highest exponent of the variable is
2. There are three main ways to solve quadratic equations: 1) to factor the quadratic equation if you can do so, 2) to use the quadratic formula, or 3) to complete the square. If you want to know how to master these three methods, just follow these steps.
FACTORING THE EQUATION
Combine all of the like terms and move them to one side of the equation. The first step to factoring an equation is to move all of the terms to one side of the equation, keeping the
term positive. To combine the terms, add or subtract all of the
terms, and the constants (integer terms), moving them to one side of the equation so that nothing remains on the other side. Once the other side has no remaining terms, you can just write “0” on that side of the equal sign. Here’s how you do it:
Since only has one set of possible factors, and , you can write those in the parenthesis: .
Then, use process of elimination to plug in the factors of 4 to find a combination that produces -11x when multiplied. You can either use a combination of 4 and 1, or 2 and 2, since both of those numbers multiply to get 4. Just remember that one of the terms should be negative, since the term is -4.
By trial and error, try out this combination of factors . When you multiply them out, you get . If you combine the terms and , you get , which is the middle term you were aiming for. You have just factored the quadratic equation.
As an example of trial and error, let’s try checking a factoring combination for that is an error (does not work): = . If you combine those terms, you get . Though the factors -2 and 2 do multiply to make -4, the middle term does not work, because you needed to get , not .