But remember, this would only be true if you're multiplying two things and you got zero as their product, then the solutions would be anything that made either one of Make this first term zero and negative one, or negative one would Another thing, try to do is, is they'll immediately say, okay, therefore x isĮqual to negative three or x is equal to negative one because negative three will Something times something is equal to negative one doesn't help you a ton. But they either make a mistake or they realize that And then they either areĪbout to make a mistake, this is actually algebraically valid. This left hand expression, say that's going to be x plus three times x plus one, and then that's going toīe equal to negative one. That add up to four and whose product is three. See something like this, let me rewrite it.
![three ways to solve a quadratic equation three ways to solve a quadratic equation](https://useruploads.socratic.org/Owlcc5uOQHeTH1HBzhjV_4063125_orig.jpg)
You'll sometimes see people use, especially when they But if can't make these things disappear, this strategy that I've just outlined is not going to be a productive one. But if you have an x term like this and it doesn't cancel out somehow, you know, if there was anotherįour x on the other side, then you could subtractįour x from both sides, and they would disappear. Then this strategy would have worked assuming that there are some solutions. In fact, it would have worked if you did not have Now, there's some cases in which this strategy would have worked. You still don't know what x is, and it's really not clear what to do with this algebraically.
![three ways to solve a quadratic equation three ways to solve a quadratic equation](https://image2.slideserve.com/4886176/completing-the-square-l.jpg)
Of negative four x minus four, but this still doesn't help you. And you could get something like this, you would get x is equal to plus or minus the square root The plus of minus of one side to make sure you're Square root of x squared is equal to, and you could try to take And now, someone might say, if I take the square root of both sides, I could get, I'll just write that down. And then what happens? On the left hand side, you do indeed isolate the x squared, and on the right hand side, you get negative four x minus four. Isolate that x squared by subtracting four x from both sides and subtracting three from both sides. So you could imagine, let me just rewrite it. People will try to go for is to isolate the x squared first. So just willy nilly, taking the square root ofīoth sides of a quadratic is not going to be too helpful. Isolate the x over here? You've pretty quickly hit a dead end. But even if this wasĪ positive value here, how do you simplify or how do you somehow Even if this wasn't a negative one here, that's the most obvious problem. Plus four x plus three is equal to the square The square root of both sides? And if you did that, you would get the square root of x squared So one strategy that people might try is, well, I have something squared, why don't I just try to take I have something on both sides of an equal sign. Why is it a quadratic equation? Well, it's a quadratic because it has this secondĭegree term right over here and it's an equation because You can find the values for which this quadratic equation equals 0, so the equation has one or two answers.- In this video, we're gonna talk aboutĪ few of the pitfalls that someone might encounter while they're trying to solve a quadratic equation like this.
![three ways to solve a quadratic equation three ways to solve a quadratic equation](https://i.ytimg.com/vi/1mbFjWt4xJ4/maxresdefault.jpg)
Solve the portion in parentheses with the quadratic formula if you can’t factor it manually. This article has been viewed 1,096,955 times. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. There are 10 references cited in this article, which can be found at the bottom of the page. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. This article was co-authored by David Jia and by wikiHow staff writer, Christopher M.