Need help with some algebra:
4x-2x^2=-12

Question

Need help with some algebra:
4x-2x^2=-12

legomyego180 · Answer

Ive rewritten this as:
$$x^2-2x-6=0$$

photon336 · Answer

step one let's get all the terms to the same time. 

$$4x-2x^{2}+12 =0$$

$$2(2x-x^{2}+6) = 0 $$

$$2*(1/2)(2x-x^{2}+6) = 0*(1/2) $$
$$2x-x^{2}+6 = 0 $$

legomyego180 · Answer

cool ok

photon336 · Answer

Yeah, do you know what to do next?

legomyego180 · Answer

I know I could use the quadratic formula, but I dont think Im supposed to

legomyego180 · Answer

My answer is in the form of $$1+\sqrt{7}$$

photon336 · Answer

let me show you another way

legomyego180 · Answer

It embarassing lol, this is for a calc II class and I forgot how to simplify

photon336 · Answer

yeah so let's go off from where we started. 

$$2x-x^{2}+6 = 0$$

legomyego180 · Answer

k

photon336 · Answer

first thing i'm going to do is multiply everything by -1 because I like to have the first term -x^2 to be positive

photon336 · Answer

$$-1(2x-x^{2}+6) = 0*(-1) => -2x+x^{2}-6$$

$$x^{2}-2x-6 = 0$$

now let's do something called completing the square. 

first thing we must do is get it in the form like this. 

$$x^{2}-2x = 6$$ 

$$ax^{2}+bx = c$$ 

now let's take  (b/2)^2 and add to both sides 

$$x^{2}-2x+(\frac{ -2 }{ 2 })^{2} = 6+(\frac{ -2 }{ 2})^{2}$$

$$x^{2}-2x+1 = 7$$

now the next part is what we do here is interesting called completing the square we re-re-write this as the following.

$$(x-1)^{2} = 7$$

$$(x-1) = \pm~\sqrt{7}$$

$$Thus~here~are~our~roots~(1~\pm~\sqrt{7})$$

legomyego180 · Answer

Ah gotcha, I always hated completing the square for some reason. Something Im going to need to practice to remember. Thank you for the help!

legomyego180 · Answer

attachment

photon336 · Answer

let's check this answer.

$$2(1+\sqrt{7})-(1+\sqrt{7})^{2}+6$$

$$2x-x^{2}+6 => (2+ 2\sqrt{7})-(1-2\sqrt{7}-7)+6~ -8+8+2\sqrt{7}-2\sqrt{7} = 0$$

legomyego180 · Answer

ok gotcha, so the you have to check the negative too?

photon336 · Answer

both would give you the same answer .

photon336 · Answer

lets me see about your other question

legomyego180 · Answer

same question

legomyego180 · Answer

Just thought it would help if you could see where I was coming from

agent0smith · Answer

So we can add basic algebra alongside fractions, in the list of things this calculus student doesn't know :P

agent0smith · Answer

@legomyego180 why do you not think you're supposed to use the quadratic formula? There's a reason it exists - it is essentially the same thing as completing the square, but takes way less time.

photon336 · Answer

yeah exactly like you don't really have to do all that work I did

agent0smith · Answer

At some point, someone realized "hey, completing the square every time like this is tedious, quite tedious indeed, why don't we find a way to make this much less a suckfest"

legomyego180 · Answer

I didnt think it would give you the same answer

legomyego180 · Answer

Yea its a long and complicated story about how I took precal and algebra 4 years ago and now im taking calculus and forgot everything blah blah blah

agent0smith · Answer

Haven't you ever seen the derivation of the quadratic formula? It literally results from completing the square on the general form of a quadratic, ax^2 + bx + c = 0.

legomyego180 · Answer

I dont think so

agent0smith · Answer

I could show you, but I don't want to. http://www.purplemath.com/modules/sqrquad2.htm or https://www.mathsisfun.com/algebra/quadratic-equation-derivation.html

agent0smith · Answer

And I don't blame you for forgetting how to complete the square. It does kinda suck.

Forgetting how to deal with fractions, though... :P