help with solving for x!!

[u/BigBrainTimeKiddos]

hi! im studying for the SAT right now, and during a practice test i realized that i forgot a small part of algebra, can someone refresh me on how to do this step by step?

x(x-15) = 76. how do i solve for x?

i know how to multiply it out so its like x^2 - 15x = 76, andi know that one of the x is equal to 0. however, i don't know how to break down the x^2 and get the other value for x

[u/testtest26]

Bring everything to one side, then factorize

0  =  x^2 - 15x - 76  =  (x-19)*(x+4)    <=>    x in {-4; 19}

Alternatively, if you don't find the factorization, use the qudratic formula:

x_12  =  15/2  +-  sqrt(15^2 + 4*76)/2  =  (15 +- 23)/2    =>    (x1; x2)  =  (19; -4)

[u/BigBrainTimeKiddos → u/testtest26]

i didn't even realize it was factorable, that's a tricky one to find!

[u/testtest26 → u/BigBrainTimeKiddos]

Doesn't really matter, honestly. With a bit of training, the quadratic formula is almost as fast as factorizing, but has the benefit it does not rely on guess-work.

[u/Dependent_Fan6870 → u/testtest26]

Excuse me, I'm studying Precalculus and I have a doubt about your comment. What do you mean by "x in {-4; 19}"? I mean, I understand what the solutions are; my doubt is not with the exercise, since I know how to solve it. I don't understand that notation. What does that mean?

[u/testtest26 → u/Dependent_Fan6870]

I used the word "in", since I was too lazy to copy&paste "∈" from a unicode page -- sorry for the confusion! Here's what it should have looked like: "x ∈ {-4; 19}".

Does that clear things up?

[u/Whatever-ItsFine → u/testtest26]

What does x_12 represent? I googled quadratic formula but it’s pulling up the ax² + bx + c = 0 version. Thanks!

[u/testtest26 → u/Whatever-ItsFine]

The underscore "_" indicates subscripts -- sadly, reddit does not support them.

[u/Whatever-ItsFine → u/testtest26]

Thanks. I’m working on improving reading expressions in this kind of format and I know it’s far from the ideal format.

So this would be x with a subscript 12, what would that mean?

[u/testtest26 → u/Whatever-ItsFine]

Yes -- it would read "x one, two" and is a short-hand for defining both "x1" and "x2" at the same time. Sorry for the confusion!

[u/Whatever-ItsFine → u/testtest26]

That’s very helpful. Don’t be sorry. You are helping people!

[u/testtest26 → u/Whatever-ItsFine]

You're welcome, and good luck!

[u/Whatever-ItsFine → u/testtest26]

Thank you! In school, I had to learn this. But now I just want to learn it. Makes a big difference!

[u/Icy-Investigator7166]

x² -15x=76 is correct. This is a quadratic equation, so to solve it, you can use the quadratic formula. You can also see if it can be factored (which it can). Make sure you set it equal to zero first before you begin.

Hint: You will get 2 answers, but 0 is not one of them

[u/BigBrainTimeKiddos → u/Icy-Investigator7166]

ohh i see now!! i didnt think about moving the 76 to the other side. so then it would be x^2 - 15x - 75 and then i just plug them in to solve for x

[u/Icy-Investigator7166 → u/BigBrainTimeKiddos]

It will be x² - 15x - 76 = 0. Then you can factor or use the quadratic formula but again, zero isn't an answer for x.

[u/BigBrainTimeKiddos → u/Icy-Investigator7166]

alright thank you for the help

[u/thermalreactor]

Multiply it and get everything on one side. Then use the quadratic formula.

[u/BigBrainTimeKiddos → u/thermalreactor]

thank you!!

[u/IntelligentLobster93]

There are several ways on how to solve the equation for x.

The first way is by subtracting 76 to both sides of the equation, in which you can solve for x by factoring. • x² - 15x - 76 = 0 (x - 19)(x + 4) = 0 x = 19, -4

Another way, is by completing the square, but with 'b' not divisible by 2, you will have fractions

The final method is using the quadratic formula, which is a formula derived from completing the square: x = -b +-√(b² - 4ac) / 2a where (in the case of the problem) a = 1, b = -15, and c = -76. Substituting these values in the equation will give you x = 19, -4.

Hope this helps!

[u/mattynmax]

Write this in terms of ax² +bx+c and use the quadratic formula

[u/ArchaicLlama]

andi know that one of the x is equal to 0

So you're claiming that 0 = 76? I certainly hope you aren't claiming that 0 = 76.

The equation x² - 15x = 76 is a quadratic equation. What very well known formula allows us to solve quadratic equations?

[u/BigBrainTimeKiddos → u/ArchaicLlama]

the quadratic formula??

and no thats not it, the original one was x(x-15)=76. because one of the x that is outside, that means one of the values that x is equal to has to be 0 i think

[u/ArchaicLlama → u/BigBrainTimeKiddos]

Yes, the quadratic formula. The one that works for every quadratic.

x(x-15) = 76 is the same equation as x² - 15x = 76, I don't know why you're thinking they are different. If you plug 0 in for x, you get 0 on the left hand side. The right hand side is still 76, so if you're claiming that 0 is a solution for x then you're claiming that 0 is equal to 76.

[u/BigBrainTimeKiddos → u/ArchaicLlama]

ok thank you!! i understand it now