Question

Hey guys, I'm relearning some Algebra and was confused about this problem. In the equation, the problem was divided by 3. This makes sense because its easier to work with smaller numbers. However, after that the negative signs swapped. Why does this happen? I remember switching signs years ago when I learned it but now I can't remember the rule as to why. Thank you so much.

Answer 1

That's optional

Explanation:

Dealing with positive numbers is simpler that's why the equation was divided by -3.

Nonetheless, you can use:

-6x² - 5x + 1 = 0 too

You will get the same answer

D = (-5)² - 4(-6)(1)

D = 25 + 24 = 49

x = [-(-5) +/- sqrt(49)]/(2×-6)

x = [5 +/- 7]/(-12)

x = -2/-12 = ⅙

x = 12/-12 = -1

Answer 2

Answer and Step-by-step explanation:

The signs didn't really "swap". Instead, the whole function was divided by -1, or we could say the function was divided by -3. That would turn:

-18x² - 15x + 3 = 0

into

(-18 / -3)x² - (15 / -3)x + (3 / -3) = 0

6x² + 5x - 1 = 0

And that gives the "swapped signs".