Quadratic Formula Explained - Detailed Step by Step Practice Problem

How to solve a quadratic equation using the quadratic formula.
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[@tomtke7351]

X^2 - 4X = 8 eq.1 complete the square.... to get to (x-2)(x-2) I need to have on the left side of equation x^2 -4x + 4 so eq.1 gets adjusted thus: x^2-4x+4 = 8+4 or (x-2)^2 = 12 eq.2 (x-2) = +/-sqrt(12) x = 2+/-sqrt(12) = 2+/-2sqrt(3) =2(1+/-sqrt(3)) ans.1 = 5.464 ans.2 = -1.464 verify X^2 - 4X = 8 eq.1 ans.1 x = 5.464 (5.464)^2 -4(5.464) =? 8 29.855-21.856 =? 8 7.999=❤8✔️✔️✔️ ans.2 x= -1.464? X^2 - 4X = 8 eq.1 (-1.464)^2-4(-1.464)=? 8 2.143+5.865=?8 7.999=❤8✔️✔️✔️ COMMENT--> when doing homework or ACTUAL work the verify step is best practice... obviously a timed test is different If rational root theorm is attempted it will fail because.. The square root of 3 is an irrational number. It is also known as Theodorus' constant, after Theodorus of Cyrene, who proved its irrationality.

[@cowboybob7093]

Thank you for 3:08 and other fundamentals - I tried factoring in my head and it was rewarding to see that method was a dead end. BTW, because of things I've learned on this channel, as soon as I saw sqrt 48 I saw 4(sqrt 3) and with the Q.F. everything fell into place - Thanks again.

[@beverleysmith8704]

I never knew that. Thanks. 👍

[@juliettehotel]

A NEGATIVE boy [-b] was deciding TO GO OR NOT GO [+/-] to a RADICAL [√] party. Once INSIDE he met a SQUARE boy [b^2] but he did NOT [-] meet the FOUR AWESOME CHICKS [4ac]. The party was OVER [/] at 2:00a.m. [2a].

[@pheelix942]

On my screen, the minor error occurs at 17.58, not 18.38. The number 2 is an elusive character, known to disappear and reappear without notice. Extra imaginary credit for those viewers who caught the error before reading the comments.

[@kevinwallace3415]

As clear as mud!

[@Oak_City_Archery]

2:38

[@OmarAli-gm5lx]

What app program are you using to draw out math problems?

[@silekiernanphotography]

It looks like Paint.

[@OmarAli-gm5lx]

@@silekiernanphotography its looks a little different to me but I just don't know

[@realSamAndrew]

Error at 18:38. You left off the factor of 2 in the long form of the solution, when you separated the+ and -.

[@warblerab2955]

It should be 2 + 2 times the squareroot of 3 and 2 - 2 times the squareroot of 3, correct?

[@realSamAndrew]

@@warblerab2955 exactly

[@art_noah]

I agree. Is this going to be fixed ?

[@realSamAndrew]

​@art_noah apparently not. It's been over 7 months with no sign of a correction or even acknowledgement!

[@latifahali6070]

Used completing the square results are the same as yours

[@user-td5hr9co1x]

Using an equation that does have an easy to solve square root would help deter anyone who is here just starting to learn up on using the Quadratic Formula. The more complex Square Roots should have its own lesson.

[@fatsteve-xthegod6711]

Lost me around 17:27. How does 4 plus or minus 4 and the square root of 3 all over 2 turn into 4 times 1 plus or minus the square root of 3 over 2?? I got extremely lost on this portion of the video.

[@maskedmarvyl4774]

You know what would be great? It would be great if you actually explained what the quadratic formula is and why it works, as well as where it came from to begin with, rather than just explaining how to plug the numbers in to find a solution without understanding or caring about the underlying principles of why the coefficients of the variables can be used to find the solution to these problems. For example, Why you are making "b" negative; Why the formula instructs the user to take the square root of b squared minus 4ac; what the discriminant actually means; and why you are putting the equation over 2a. You know, actually understanding what is going on, and why. You explained how to plug numbers into the quadratic formula and to have faith that it will find the answer; but you never explained the formula itself.

[@cowboybob7093]

This channel has another clip titled: _The Quadratic Formula - Understand In 7 Minutes_ It may help, but it doesn't explain things like "why is `b` negative" etc." I'm not a mathematician or a math historian. I think what you're looking for is from history and IMO it looks like a mathematician who ran into the shortcomings and decided a generalization was needed to cover all QE. I don't think they started with the leap from FOIL to 'b is negative right there' but instead worked their tail off with informed trial-and-error for a few days. In a way it's like Newton and Einstein working on orbits. Einstein was doing it because Newton's formula didn't work for Mercury, close but no cigar. After he was proven correct his formula was applied to the other planets and was found to be more accurate even though Newton's was accepted to be adequate. A difference here is that when a problem requires the QF it has no simpler solution, when Newton's formula is applied to orbiting bodies it gives a close-enough approximation.

[@mikepublic111]

In less than the time it took you to type your complaint, you could have done a web search on 'history of the quadratic formula' and gotten an answer. The fact is there is no single answer. Some people attribute it to a Hindu mathematician, others attribute it to a European mathematician, others attribute it to a Persian mathematician, and still others attribute it to ancient Babylonian mathematicians. Apparently it can be derived from the 'completing the squares' method.

[@maskedmarvyl4774]

@@mikepublic111 , You've just explained more than the original poster did.

[@GiorgioSemprevivo]

First comment again. 😁

[@rebeccadee4107]

I must be third in line for this lecture!

[@pieterjlansbergen6988]

Took me about 30 secs. without even pen and paper.

[@robmartin5518]

so my motto is why have 50 tools for 50 jobs when you can do the 50 jobs with just one tool so long as the quality is equal or better. Translate that to this why not just use the quadratic formula? (I am of course assuming this will work for any kind of equation so long as it is in the proper format as shown)

[@davidking7045]

Oh Dear 😂

[@jimroe850]

Best way to remember is to hum POP GOES THE WEASEL while saying it - you will NEVER forget the formula !!!!!🤣🤣🤣🤣🤣🧐🧐🧐🧐👍👍