Solving Without Factoring or Quadratic Formula

[mrhtutoring]

Here's yet another way to solve a quadratic equation.

[Info_rare]

Your handwriting and the sound of the marker are so soothing

[markrobinson]

This is suspiciously close to completing the square. Keep up the good work.

[Kamabushi]

this guy does things outside the box, amazingly refreshing

[sylvesterogbolu-otutu]

Mr. H, you should inform your subscribers that what you are doing is simply a modified Viete's Theorem.

Given:

2x^2 - 24x - 216 = 0

a = 2, b = - 24, and c = - 216

According to Viete's Theorem;

Sum of Roots = -b/a

And;

Product of Roots = c/a

Sum of Roots = - (-24)/2 = 24/2 = 12

Product of Roots = - 216/2 = - 108

The factors of - 108 that sum up to 12 are + 18 and - 6

(-6) × (18) = - 108
(-6) + (18) = 12

Therefore, the roots of the given quadratic function are:

x = - 6 and/or x = 18.

[tedvillalon]

I was hired to teach middle school history but was asked to teach math instead( I had 18 hr of undergrad math and computer science). When solving a question sumilar to this, the bells and whistles came out. Look how beautiful it is! I hadn't done thatwork in 30 years but it all came back.

[ThomasTheThermonuclearBomb]

I always wondered if you could find solutions using the vertex formula, this is amazing!

[ohSpezy]

The famous Professor Po-Shen Loh's method

[rhinooningo]

This is interesting and I've never seen it before. Is this something relatively new, or did it just escape my awareness since my first algebra class in junior high school?

I don't see any compelling advantage of it over using the quadratic formula, completing the square "manually, " or even factoring, but I haven't tried any problems with it yet.

Thank you for sharing this (and all of your other excellent content). I wish I could have learned from you when I was still teaching algebra because I think much of what you present would make me a more effective teacher.

[christianfunintuscany]

This method is basically a change of coordinates that move the origin to the vertex of the parabola so that the quadratic equation turns to have the b value equal zero

[amazer]

There is need of a save button in YT Shorts man.😭

[peacefulgarden-jo]

Wow, this is new and amazingly working!
So simpler than factoring when there are so many factors for c and much easier than using quadratic formula

[Tigermaster]

2x^2 - 24x - 216 = 0 I dividing by 2
x^2 - 12x - 108 = 0 I adding and subtracting 36 to the left side
x^2 - 2*x*6 + 36 - 36 - 108 = 0
(x - 6)^2 - 144 = 0
(x - 6)^2 = 144
1. x - 6 = 12 -> x = 18
2. x - 6 = -12 -> x = -6

[karpholmes]

I feel like the quadratic formula, completing the square, and whatever one where you multiply c by a and divid a by a in the beginning, are much faster. I can do the above in less than 30 secs without a calc and this seems like much more work.

[fizzle]

This is just modified quad formula. At the start he divides b by -2(a) and then he solves for t using (b^2 - 4ac)/4. Still pretty cool but it can get a little messy when solving free fall and area problems.

[zzwcinq]

Did statistics for my undergrad and now post grad. in analytics, and i'm just learning about this trick. Thank you so much. I'm dealing with complex numbers, and this is just a genius short -cut

[KaushalDhruw]

Nice simplification of the quadratic root formula. Love it.

[Tejas]

Man u are a great mathematician this took like 2 sec while the basic method takes 2 min

[agrocassiano]

x^2 - 12x - 108 = 0
x^2 = 12x + 108

Fórmula *X = b/2 + - ^[ (b/2)2 + (c) ]*

X = 6 + - ^[ 36 + 108 ]
X = 6 + - ^[ 144 ]

*X' = 6 + 12= 18*
*X" = 6 - 12 = - 6*

Parabéns Professor, sucesso sempre. 🎉

[khaledf]

Step 1 dived every thing by the x^2 coefficient to make a=1
Step 2
This the special case of the quadratic formula when a =1
Solution =b/-2 +/- sqrt(b^2/4-c)