(4x + 5)(x + 1) = 0 Can You Solve This ALGEBRA EQUATION?

[@robbusey7827]

If I had only added "senior math" before I finished high school 62 years ago, I might have been successful when I tried engineering in college. Now when I watch documentaries about building the Golden Gate bridge and the Eiffel tower I'm reminded to look for new mental challenges at age 80. Don't give up on your dreams when you're a frustrated 18-year-old. The people who say they can or they can't are both right. Of all sad quotes of mice or men, the saddest are these: "It might have been."

[@flagmichael]

First year algebra. Either (4x+5) is zero or (x+1) is zero. Ten seconds at most.

[@jeffpowers1979]

well isn't 0x0 =0

[@PraiseDog]

@@jeffpowers1979 Well yes, but x can't be equal to two different things at the same time.

[@redblack8414]

I used the quadratic formula instead of assuming that one or both binomials is or are equal to zero. I had forgotten about that. I studied algebra in the 60s and early 70s. Your channel is really interesting.

[@ishtiaqahmedkhan2328]

Nice thing is that it refreshes olden school time era!

[@BlackLadyRules]

Love these videos. It’s not “being that”. It’s “since.”

[@Stylux-z1p]

[4x + 5 ] [x + 1] = 0 4x[x + 1] + 5[x + 1] = 4x² + 4x + 5x + 1 = 0 4x² + 4x + 5x + 1 = 4x² + 9x + 1 = 0 ---> looks like a quadratic equation the first term of the trinomial has a power of 2 , that means the equation has to solutions reverting back to its original form : [4x + 5 ] [x + 1] = 0 [4x + 5 ] [x + 1] = 0 --> property of multiplication if one of the factors of the multiplication is zero the product is also zero -> a * 0 = 0 , 0 * b = 0 4x + 5 = 0 4x + 5 - 5 = 0 - 5 4x = -5 4x / 4 = -5 / 4 x = - 5 / 4 --> first solution x + 1 = 0 x + 1 - 1 = 0 - 1 x = -1 second solution The two solutions of the quadratic equation { -5 /4 , -1} ---> ANS proof by substitution: [4(-5/4) + 5 ] = 0 [(-1) + 1] = 0

[@gregpoehlein6654]

The Zero Product Property can be derived Algebraically. For the left term, divide both sides of the equation by (x+1), which yields (4x+5) = 0/(x+1). Zero divided by anything is zero, so the equation becomes (4x+5) = 0. Likewise, divide both sides by (4x+5), which yields (x+1) = 0/(4x+5). This becomes (x+1) = 0.

[@dazartingstall6680]

I'm not so sure. The Zero Product Property states that if xy = 0 then either x, y *or both* must be zero. Your method works fine if only x or only y is zero, but if both are, we end up with each being equal to 0/0, which is undefined.

[@gregpoehlein6654]

@@dazartingstall6680 - Note that I said derived, not proved. As long as the variables remain unresolved (in other words, they are not actually equated to 0, we can divide 0 by the variable and we are fine. And since we resolve only one variable at a time, it works. In other words, either x=0/y, or y=0/x, but not both at the same time. I'm really only deriving the result of the Zero Product Property, not proving it. And deriving the result is not the same thing as proving or defining it. Semantics, perhaps, but it does work.

[@dazartingstall6680]

@@gregpoehlein6654 That's a good distinction. I withdraw my objection

[@jayden_the_bullnguyen1002]

Wonderfully explained❤

[@oldrrocr]

if your point is to "get to the point", the lesson starts at 14:00. right?

[@robertstuart6645]

When the quadratic equation is in the parenthetical form, as is the case here, simply set each parenthetical expression "=0" and solve for "x".

[@marccracchiolo4935]

Great video thanks for sharing it’s so easy to forget this stuff

[@YvanStansfeld]

(4x+5)(x+1)=0 =4x^2+9x+4x and the other way is 4x+5=0 -5. -5 x= -5/4 x+1=0 -1. -1 x=-5/4. x=-1 Then combine the like terms and coefficients (4x+5)(x+1) = 4x^2+9x+5

[@YvanStansfeld]

68x39= 2,652

[@YvanStansfeld]

Do 70x39= 2,730 then multiply the base number 39x2 =78 Subtract 2,730 - 78 = 2,652 that's how people will do it in their head lightning fast Vehicle trick from India Wish it was taught here in schools here. Thank-you

[@YvanStansfeld]

Vedic I meant lol

[@ehonwasamuel8158]

(4x + 5)(x +1) = 0. Expand to remove the brackets and collect terms: 4X x X = -5 -1 4X = -6 X = - 6/4 X= - 1 1/2 .

[@panlomito]

Quadratic equation ax² + bx + c = 0 always have 2 solutions for y = f(x) = 0 according to John. That is not correct because the parabola can be fully above or below the x-axis (discriminator D = b² -4ac < 0) resulting in NO solutions for y = f(x) = 0, the parabola just touching the x-axis with the top (D = b²-4ac =0) resulting in just ONE solution for y = f(x) = 0 or with the TWO solutions for y = f(x0 = 0 when D = b²-4ac > 0 resulting in 2 crossings with the x-axis. For example: 2x² + x + 4 = 0 so a = 2 b = 1 and c = 4 -> D = (1)² - 4 . (2) . (4) = 1 - 32 = -31 so there are no solutions for y = f(x) = 0 with a > 0 this top down parabola is fully above the x-axis. xtop = -b / 2a = -(1) / 2 . (2) = - 1/4 and ytop = f(-1/4) = 2 . (-1/4)² + 1 . (-1/4) + (4) = 1/8 - 2/8 + 4 = 3 7/8 and top at ( -1/4 , 3 7/8 ) Or -x² - 4x - 4 = 0 so a = -1 b = -4 and c = -4 -> D = (-4)² - 4 . (-1) . (-4) = 16 -16 = 0 so there is only 1 solution for y = f(x) = 0 with a < 0 this top up parabola is just touching the parabola with its top at xtop = -b / 2a = -(-4) / 2. (-1) = 2 and top at (2,0) and the rest of the parabola under the x-axis.

[@PraiseDog]

I see a lot of comments with people trying to make things overly complicated. Always look for the simple solution to problems, don't complicate things when you don't need to. You have a product of two brackets. What makes one zero, what makes the other zero? Done, move on to the next problem.

[@panlomito]

This quadratic equation is too easy again, already factorised for our convenience: x = - 5/4 or x = -1 Going back: 4x² + 5x + 4x + 5 = 0 so the unfactorised equation will be 4x² + 9x +5 = 0 with a = 4 b = 9 and c = 5 How DO we factorise this? First step a/a . x² + bx + ca = 0 so x² + 9x + 20 = 0 factorised in (x+5)(x+4) = 0 and now we divide the answer by a = 4 So (x + 5/4).(x + 4/4) = (4x + 5).(x + 1) = 0 Tadaaaaaa!

[@btpcmsag]

Sorry, I don't understand your "steps "

[@panlomito]

@@btpcmsag It is a nice procedure to factorise quadratics when a is not 1 with a in ax² + bx + c = 0 The procedure starts with dividing a by a : (a/a) . x² = 1.x² = x² and multiplying c with a : c.a You now have a modified equation that is easier to get factorised: x² + bx + c.a = 0 After factorising this modified equation you get (x+d).(x+e) = 0 Last step is to bring a back in the factors by multiplying x with a : (ax + d).(ax + e) = 0 For example: 6x² - 5x - 4 = 0 modified: (6/6)x² -5x - 4.6 = x² -5x - 24 = 0 factorised in (x - 8).(x + 3) = 0 and modified back to (6x - 8).(6x + 3) = 0 or (3x-4).(2x+1) = 0 Answer x = 4/3 or x = -1/2 Check with abc-formula: D = b² - 4ac = (-5)² - 4.(6).(-4) = 25 + 96 = 121 positive so 2 solutions xtop = -b / 2a = -(-5) / 2.(6) = 5/12 vertical symmetry-axis of parabola x = xtop delta = V(D) / 2a = V(121) / 2.(6) = 11/12 distance between xtop and the two solutions for y = f(x) =0 x = xtop minus/plus delta so x1 = 5/12 - 11/12 = - 6/12 = -1/2 and x2 = 5/12 + 11/12 = 16/12 = 4/3 check !

[@thomasharding1838]

YES! (The question is "Can You Solve?, not 'What is X?' But for those who misread the question, X = -1 and -5/4)

[@jeffpowers1979]

I still want to know how you came up with -1 and -5/4 other than just saying that. The Logical question is What is X and how do you get the value

[@thomasharding1838]

@@jeffpowers1979 For (4x + 5)(X + 1) to equal 0, either 4x+5 or x+1 has to equal 0. Therefore 4x + 5 = 0 resolves to 4x = -5 => x = -5/4 or, x + 1 = 0 which resolves to x = -1. But still, the question is "Can You Solve?" not "What does x equals".

[@richardhole8429]

1. Quadratic 2. Yes Technically you did not ask for the two solutions but I did then in my head in a couple of seconds.

[@russelllomando8460]

Got both of them. I had each = 0 and solved for x. - 1 and -5/4 Thanks for the fun.

[@nadiaconseillant8616]

4x^2 + 4x + 5x + 5= 4x^2 + 9x + 5

[@YvanStansfeld]

78x32= 2,496

[@billmclaurin6959]

How can we justify to assume that both (4x+1)=0 and (x+1)=0? only one of the expressions needs to be zero for the product of the two expressions to equal zero.

[@henkhu100]

That's why he says "or" has to be zero.

[@chrisdissanayake6979]

(4X+5)(X+1)=0 Either (4X+5)=0 OR (X+1)=0 If 4X+5=0, X=-5/4 If X+1=0, X=-1 X=-5/4 OR X =-1

[@ralphmelvin1046]

That was a good way to end it I thought you were going to stop with the 4x=-5 x=-1

[@chalapathitk8972]

Good explanation, tq. Haribol Harekrishna

[@dazartingstall6680]

(4x + 5)(x + 1) = 0 If 4x + 5 = 0 then 4x = −5 x = −1.2 If x + 1 = 0 then x = −1 [edited for a stupid presentational mistake]

[@johnmarchington3146]

It's a quadratic equation and x's two values are -5/4 and -1

[@jeffpowers1979]

Just show us how to find the value of X

[@davidbrown8763]

I did this in my head, but thanks for the challenge.

[@mylittlepitbull3143]

I KNOW THE ANSWER! I KNOW THE ANSWER! (Hand up in the air frantically waving to the teacher) The answer is... YES. I can solve.

[@thomasharding1838]

Poor Teacher! He got stuck with TWO Smart Ass comments within ten minutes of each other. I didn't see your comment or I would have held off on mine. BS I would hold off!! Not in THIS Lifetime. But at least only one of us was standing up waving our hands!)

[@panlomito]

Notice that NO is also a perfect answer if you can not solve.

[@mylittlepitbull3143]

@panlomito You are correct and you have now graduated to the next level.

[@btpcmsag]

x=-1, or x=-5/4

[@sdcashman45]

FOIL method

[@geogeo6071]

First FOIL and then use the quadratic equation.

[@pandurangaraonimmagadda9966]

x=-1or x=-5/4

[@seibertmccormick184]

-1.25 or -1 It took a few seconds.

[@mollymam7153]

X=-1 or X=-5/4

[@josephlaura7387]

X= -1, x= -5/4

[@manjeet-tp9di]

-5/4 ,-1

[@AssuredSystems]

Quadratic Equation wkth X=-5/4 and x=-1

[@giannaleoci2328]

4x+5=0 x=-5/4 x+1=0 x=-1

[@iamrisa18]

Just by looking at the problem..I already knew the answers right away 😌

[@valerierobertson4912]

4

[@ramesankd1604]

Nocammet*s

[@ArthurAyala-n2j]

x= -1 x= -5/4

[@Christopherdpenha]

Yes my dears, this John is JACKASS, specialise in make a mountain of a mole hill.

[@Fensmiler]

(4x+5)(x+1) (5x+6) I don't know

[@iamrisa18]

There are two solutions: 4x+5=0 4x=-5 x=-5/4 Or x+1=0 x=-1

[@dannichols6261]

@@iamrisa18 Yes, the 'problem' is already factored for us! Anything times zero equals zero. Therefore anything that makes either factor equal zero reveals one or another solution.

[@iamrisa18]

@@dannichols6261 exactly 💯 👏🏾

[@monkeydigs6696]

-1 I did this mentally lol. I’m just that cool 😎

[@creeperchow2949]

Your name is Monkeydigs you are already cool

[@creeperchow2949]

Most of us did it memtaly

[@creeperchow2949]

I can't believe it spelled that wrong

[@monkeydigs6696]

@@creeperchow2949 thanks I suppose but I was being sarcastic

[@sekharb6651]

X=-5/4 ,-1

[@teweldemebrahtu9901]

You like too much talking ,, why not answer shortly?

[@jjmcq2327]

Dude like get like your own channel, and he did answer quickly.

[@YvanStansfeld]

Thanks man for standing up for me ,math is my passion appreciate you. I'm gonna start mental vedic mathematics I learned in India introduce to schools hopefully become a professor you know Anyway thanks brother .

[@YvanStansfeld]

479,678,349x7= 3,357,758,443

[@YvanStansfeld]

(77x4)x(2)÷4=154

[@richardhole8429]

Why don't you crank up the speed to 2x or more?

[@ArtVanAuggie]

Don't talk, THINK. Make one of the polynomials zero. Minus 1 or minus 1.25 are blatantly obvious.

[@jimdugan7240]

X = -1

[@creeperchow2949]

I am 14 and it took me 10 seconds to figure out that x is equal to -1 To bad I suck at math only when I am at school

[@dannichols6261]

Except that it's not ONLY equal to -1!! There is another valid solution: x=-5/4 also solves the equation. Should have taken 11 seconds.

[@johnadams1657]

why would you want to solve for anything that equals ZERO?? why why ??

[@bulwinkle]

Comment for the algorithm.

[@vasanthosangadi2896]

X= -1 or X = -5/4🙏🇮🇳🚩

[@harrymatabal8448]

-5/4 or -1. But it took you more than 16 minutes. Dont give up your day job

[@dawnradel9008]

X=0

[@romanwondimu8696]

0

[@matthewfrench8839]

Snooz……..,,😞this is why I never liked math class. Boring teachers! Most math teachers did not know how to make math come alive! Total turn off☹️🇺🇸😇

[@karlapenny4424]

I guess were both struggling😂😂😂😂😂😂

[@georgecattani7199]

X=-5/4. X=-1

[@JosephGelis]

x = -1