How to Solve Quadratic Equations by Factoring (NancyPi)

MIT grad shows how to solve any quadratic equation by factoring. To skip to the shortcut trick, go to time 6:11. Nancy formerly of MathBFF explains the steps.

The shortcut trick ("The Magic X") helps you factor any tough quadratic that doesn't begin with x^2 but instead begins w/ 2x^2 or 3x^2, or 4x^2, etc, so you can then solve.

1) IF QUADRATIC STARTS WITH X^2: It's faster to use the normal method for factoring in this case: trial and error. Ex: x^2 + 4x - 12. Find 2 numbers that multiply to the last number, -12, AND that add to the second coefficient, positive 4. First make a list of all pairs of #s that multiply to -12. Then check which pair also adds to 4. Write factors & solve by setting each = 0. Solve for x.

2) IF QUADRATIC STARTS WITH 2X^2 OR 3X^2 OR 4X^2, ETC:
A) First check if leading coefficient (2 or 3 or 4, etc) is an overall constant you can factor out of every term. If it is, factor it out first, then use Method #1 above to factor the X^2 expression that's left. Set factors = 0 & solve.
B) If a constant can't be factored out evenly from every term, it'll be faster & easier to use shortcut "magic X" method instead of Method #1. See it explained at time 6:11 in video. Set factors = 0 & solve.

[Jana-lyuw]

I have been unable to understand this lesson for months despite having two teachers explain it to me several times, but only 3 minutes into the video, I had understood what I could not understand for months in just one second. You are a GENIUS. Thank you so much, love from Egypt.

[zelo]

Photomath has a heart attack when you try to scan these problems so this really helps.

[stupendouspickle]

Fnished high school 20 years ago. Studied humanities and worked for 17y, changed fields and now back at school, taking math refresh course. Didn't understand factoring back then and didn't understand it for the past 3 weeks... You saved me! thank you so much.

It's not just the teaching, I know video editing is time consuming!! Thank you so much!!

[DOiTAGAiN]

Thank you for all of your videos. You are truly a blessing. Thank you 🙏

[chelseycampbell]

I have watched almost everyone on TikTok try to teach me how to do this. I finally found you and your voice is truly so calming, and it makes me feel so calm during a stressful time at exam week.

[aidanforden]

This helped me more than Khan Academy. Thank you.

[matthewwest]

I think, out of all the maths channels, NancyPi is by far the best! She talks through it step by step which allows you to actually keep up and understand it. Most maths channels dive straight in, go far too fast and don't talk through it step by step.

Keep up the good work!

[bryantayui]

OMG looks like she's doing that math while mirror writting. This must be mind boggling.

[howlingmedia]

I got my GED yesterday TY to YouTube teachers with their help in posting these educational videos :)

[MyWyze]

Glad you were able to get all your old videos back! I hope to see you continue to with new content!!

[edgarjimenez]

Love NancyPi! She makes learning and re learning math easy to follow…

[dharvell]

Wow... 27 years out of school and this FINALLY makes sense! It didn't help me any that my instructor didn't speak English very well. When being taught the art of solving "quadratic equations", we were all just staring, glassy-eyed at the board while our instructor droned on about "quad-e-reddic eck-wishuns". Thanks for making this look easy.

[mathewthomas]

Also how did this girl find out a strategy that simple yet so good. The magic X made life so much easier.

[ChrisHobson]

Thanks for sharing! I hadn’t done these in over twenty years and this refresher was very helpful.

[gedenirfiorese]

Your videos are amazing. Easy to follow through. They are helping me a lot to review factoring for college algebra.

[jaipadhi]

Exactly as I was taught in school .. back in 1977-78! Thanks Nancy for reviving memories..

[lexiegrl]

I really love your channel and it really helps me because I know it may seem like a small thing, but I like how we’re able to see a person and not just hands writing, because I take in a lot when I’m learning. I can visually see you writing and I can also see words coming out of your mouth which doubly cements the information I’m intaking so thank you so much for that. I also like your setup with that clear board and honestly even the pink color keeps a girl like me engaged, who is allergic to math. Thank you for all your videos that are concise and gentle. I’m taking calculus again which I failed and I’m hoping to really make a comeback. You videos give me hope. Thank you.

[ikolatasiidsdd]

Hahahah you are the guardian angel of finals week.

[JohnAnderson-yyze]

This was a life-saver. I always wondered how my Ti-36x Pro did it... But now I can do it without its number solver. Thank you very much for taking out your time to show us the steps!

[AnwarHussainFaruqh]

Greatly compact illustration, in a clear step by step clarity, dear Nancy 1
Thank you so much !
Appreciate your kind contributory help for all the fellow humanity through maths !