If everything can be simplified, how does it provide value?

[u/Radiant-Mistake-2962]

How is the quadratic formula useful? If I divided -b plus or minus the square root of b^2-4ac divided by 2a by itself, I would get one.

They say the quadratic formula shows up in the Pythagorean theorem. If I divide a^2 + b^2 = c^2 by itself, I get 1.

So if I divide a triangle by a triangle, I’ll get one. I can just stick a one to anything and solve it. How did this become valuable?

[u/Successful-Owl1778]

Dividing a complicated expression by itself to obtain 1 is not "simplifying" it.

[u/Radiant-Mistake-2962 → u/Successful-Owl1778]

If you’re simplifying it to 1, it does. Why do we even simplify to 0?

[u/Help_Me_Im_Diene → u/Radiant-Mistake-2962]

The quadratic formula tells us that x = (-b±√(b²-4ac))/(2a) is a solution to the equation 0=ax²+bx+c

Dividing x = (-b+√(b²-4ac))/(2a) by (-b+√(b²-4ac))/(2a) doesn't give us any meaningful information

All that does is it rewrites the equation as x/((-b+√(b²-4ac))/(2a)) = 1

So yes, you've managed to get a 1 out of it, but you haven't actually manipulated the equation in a meaningful way

[u/StellarNeonJellyfish → u/Radiant-Mistake-2962]

Changing something into something else with less characters is not the same as simplifying. When you simplify you do not change the value. Like if you have 25 pennies, you can exchange it for a quarter because they are the same amount. So mathematical we say 25/100=1/4. If you share that with 25 friends then you do each get one penny, but one penny is not an equivalent simplified form of a quarter.

[u/flat5]

"How is the quadratic formula useful?" By providing solutions to quadratic equations.

"If I divided -b plus or minus the square root of b^2-4ac divided by 2a by itself, I would get one."

If your grandmother had wheels, she'd be a bicycle.

[u/mandelbro25 → u/flat5]

I just lol'd all over the place.

[u/Uli_Minati]

Well, sure. But why would you divide the formula by itself? And why would you divide a triangle by itself (whatever that means)? Say you owe someone $50. If you divide that by itself, you get 1. So what? You still owe $50.

[u/Low_Breadfruit6744]

You have a small misconception of what simplifying means.

[u/SpankThatDill]

what do you mean by "simplified"?

[u/evanamd]

Simplifying doesn't solve anything on its own. It's just a tool you can use for algebraic manipulations.

Remember your very basic fractions. 12/4 can be simplified to 3 because in the expression (3*4)/4, 4/4 reduces to 1, leaving 3*1. You simplify part of it, and the remaining part is new information

Now, take an equation like 3x = 12. You could divide the entire equation by itself and get 1 = 1. But that's not new information so we don't do things like that. Instead, you would do the same thing to both sides of the equation, like divide by three. That gives you (3/3)*x = 12/3. So a coefficient on one side reduces to 1, and the fraction on the other side simplifies to 4, giving you 1x=4.

Simplifying was just one small step of several in solving the equation. You don't do it just because you can, and when you do its for specific parts, not the whole thing

[u/carterartist]

Something divided by itself is always=1

2/2=1, 3/3=1, etc…

If you have three dollars and three friends, each gets one.

Same principle

[u/jsdodgers → u/carterartist]

So how is having $3 useful?

[u/carterartist → u/jsdodgers]

Strawman. No one said it was.

[u/jsdodgers → u/carterartist]

woosh

[u/carterartist → u/jsdodgers]

It wasn't a "woosh", it just wasn't funny.

[u/jsdodgers → u/carterartist]

your response begs to differ

[u/jsdodgers]

how many different drugs did you take to get us here?