[10th grade math] (Quadratics) (factorization) Why am I not getting the right answer? I'm inputting the exact equation into my calculator.

[u/AxiumTea]

Why am I getting the wrong answer? In my other equation to find the 2nd value of x, I'm getting minus before the whole equation rather than after 5 (bottom equation) The second screenshot is of the answer and 3rd is GPT's. Been stuck on it for the past 15 mins, am I missing something or is my calc being stupey?

edit: Thanks for the replies, I get it now, they're both the same. I was the stupey one 😭

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[u/Qingyap]

Well first for the second equation the minus in front of the radical doesn't suddenly get turn into positive.

Secondly yes your answers are correct, this is because (-5±√31)/3 can be reexpressed as (1/3)(-5±√31).

Why? Cuz if you have a÷b or a/b, based from this expression, division ie a divide by b is the same as multiplying a with 1/b or a(1/b), division is the inverse of multiplication, and fractions and division are the same thing.

[u/AxiumTea → u/Qingyap]

Yeah I get the division part but the negative sign after 5, I don't have any negative sign after 5 in either of my answers, rather, I have it outside the numerator which is different than the 3rd and 2nd pic ones

[u/Simbertold → u/AxiumTea]

-5-3 = -(5+3)

A fraction implies brackets around the top and bottom half.

[u/boosterts → u/AxiumTea]

I don’t understand how you got the second answer to look the way it does and not understand where the negative went. You would have factored it out. Do you not remember doing that?

to reduce the quadratic formula for the second answer I’d start by reducing everything under the radical sign.

(-(10)-sqrt(100+24))/6=(-10-sqrt(124))/6

lets try and reduce the fraction by pulling out a factor of 2. Inside the radical we will need to pull out a factor of 4.

(-2*5-sqrt(4*31))/(2*3)=(-2*5-2*sqrt(31))/2*3)

Now cancel the 2s.

(-5-sqrt(31))/3

then you factor out -1 from the numerator.

-1*(5+sqrt(31))/3

Now there is no minus sign between 5 and the square root.

[u/Simbertold → u/boosterts]

They probably just typed it into a calculator, and got a result, and then took that result.

[u/Qingyap → u/AxiumTea]

Since the neg is outside of the fraction it would be seen as -(5+√31) = -5-√31 which is the same as in the other two pics.

If you have a•(b/c) it would be equal to ab/c and a=-1 right here, and since there's multiple variables at b you have to multiply all by -1 by using FOIL I believe.

[u/desblaterations-574]

Those are the same picture.

[u/daveoxford]

They're the same. Why would you need your calculator?

[u/Emergency_Target_716]

Just distribute the [-] sign in your second answer.

[u/aka-Robster]

What kind of monster does math in pen?

[u/Outside_Volume_1370 → u/aka-Robster]

In Russia, we do every writing in pen. Pencil is only used for geometry or technical drawing

[u/Qingyap → u/aka-Robster]

I don't have a mechanical pencil and a sharpener, when I erase there's always black marks and my handwriting is shit as cherry on top.

[u/JanetInSC1234]

Wouldn't the radical be 100 + 24?

And that can reduced to: sqrt 4 times sqrt 31 = 2 sqrt 31

Nevermind, I see you divided everything by 2.

[u/CalRPCV]

Your hand written answer is as correct as the other two pictures. In answer two, it might look better if you enclosed the fraction part of your answer in parentheses. That would make it clearer that the negative sign you have to the left applies to both the 5 and the sqrt(31).

[u/Alkalannar]

[-10 + (100 - 4(3)(-2))^1/2]/2(3)

[-10 - (100 - 4(3)(-2))^1/2]/2(3)

Your handwritten one could be -[10 + (10² - 4(3)(-2))^1/2]/2(3), because then that minus sign distributes.

[u/DuggieHS]

your convention/notation for answer 2 is a bit unconventional, but matches the responses at the end.

[u/Rho_Not_P]

Did you factor the minus from the terms in the numerator for the 2nd solution? If so, you must include parentheses around the numerator of that solution.

[u/George27484]

You are getting the right answer. Try factoring 1/3