Armadillo Run forum

JustcallmeDrago wrote:x^2 + 4ax + 4a^2 - b^2

:evil:

If you're ever stuck on factoring a binomial you can always resort to the quadratic formula. It's obviously not the best method to use normally but can save you on a test. For this one:

-4a +- sqrt(16a^2 - 16a^2 + 4b^2) / 2
(-4a +- 2b)/2
-2a +- b
so your roots are -2a + b and -2a - b so your factors are (x + 2a + b)(x + 2a -b)

TSchultz wrote:x^2 + 4ax + 4a^2
(x+2a)^2

OMG Why did I think that was impossible!?!?! Well, thanks!

& Ike, thanks a lot for that tip. I'd probably heard that from my teacher, but why would anyone listen to them over one's forum pals? ;P

Solve by completing the square: (Teacher says answers need to be exact)

OK NOW SKIP TO BOTTOM.

2x^2 - 5x - 4 = 0

A = 2
B = -5
C = -4

Divide by A.

x^2 - (5/2)x - 2 = 0

B = -5/2

Rewrite as x^2 + bx on left side (basically move C to other side.)
x^2 - (5/2)x = 2

Add (B/2)^2 to each side.

x^2 - (5/2)x + (5/4)^2 = 2 + (5/4)^2
x^2 - (5/2)x + (5/4)^2 = 2 + 25/16
x^2 - (5/2)x + (5/4)^2 = 32/16 + 25/16
x^2 - (5/2)x + (5/4)^2 = 57/16
x^2 - (5/2)x + 25/16 = 57/16

Make left side into binomial.

(x - 5/4)^2 = 57/16

Square root the entire thing.

x - 5/4 = +- sqrt(57)/4

x = 5/4 +- sqrt(57)/4

5/4 + sqrt(57)/4
1.25 + ~7.55 / 4
1.25 + 1.8875

One of the answers is ~3.1375

I thought I did it right, but when I plug in 3.1375 into 2x^2 - 5x - 4 = 0

2(3.1375)^2 - 5(3.1375) - 4 = 0
2(9.84390625) - 15.6875 - 4 = 0
19.6878125 - 15.6875 - 4 = 0
4.0003125 - 4 = 0
0.0003125 ~= 0

Close enough.

Is the "exact" way to write the answer:

5/4 - sqrt(57)/4 & 5/4 + sqrt(57)/4

Or do I have to simplify?

Hey, look at me answering my own question!

5/4 - sqrt(57)/4
sqrt(25)/4 - sqrt(57)/4
sqrt(25 - 57)/4
sqrt(-32)/4
4i * sqrt(2) / 4

i * sqrt(2)

and

5/4 + sqrt(57)/4
sqrt(25)/4 + sqrt(57)/4
sqrt(25 + 57)/4

sqrt(82)/4

sqrt(25)/4 - sqrt(57)/4
sqrt(25 - 57)/4

Square roots don't work that way.
Just leave it as (5+-Root(57))/4

Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes

NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes :? :?

-.- shut up. I actually never pay attention in class.

JustcallmeDrago wrote:

NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes

-.- shut up. I actually never pay attention in class.

Sorry, didn't want to offend you! Just really being very surprised.
In fact, math is very important subject, because it helps to involve logic and thinking.

NickyNick wrote:

JustcallmeDrago wrote:

NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes :? :?

-.- shut up. I actually never pay attention in class.

Sorry, didn't want to offend you! Just really being very surprised.
In fact, math is very important subject, because it helps to involve logic and thinking.

Whoops, sorry, I meant to say "-.- shut up. :P ". I am not offended.

Yeah, my schooling is strange because my math is the lowest level of all my classes, with English being my hardest and most advanced class, although I am best at math and worst at English.

What emphasis is put on English, ... or the equivalent where you live?

NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes

Damn. Kids do Precalc at 12?
Damn. That means they'll have done Multivariable Calc by 14.
I thought I was ahead in math, but apparently I'm barely above average in Russia.

TSchultz wrote:Damn. Kids do Precalc at 12?
Damn. That means they'll have done Multivariable Calc by 14.
I thought I was ahead in math, but apparently I'm barely above average in Russia.

In Ukraine
In fact, I'm studying in physical-mathematical lyceum, one of the best in the whole country. Maybe, guys in ordinary schools are not so good in math, but the school programs for us and them are similar. It means that they study all this stuff in 12 too.

NickyNick wrote:In Ukraine
In fact, I'm studying in physical-mathematical lyceum, one of the best in the whole country. Maybe, guys in ordinary schools are not so good in math, but the school programs for us and them are similar. It means that they study all this stuff in 12 too.

Ah! sorry.
I'm 4 grades ahead of people in my class, and they are all 1/2 years ahead of where kids normally are.
So Kids in Ukraine 5/6 years ahead of in the USA? That's scary.

How do I continue completing the square from y=3(x - 9)^2 - 108?

XD

I really suck at maths lol

y = 3(x-9)^2 - 108 = 3((x-9)^2 - 36) = 3((x-9)^2 - 6^2) = 3(x-15)(x-3)

I worked it out just before you posted lol

how about this

when X^3 + pX^2 + p^2x - 36 is divided by x-3 the remainder is 21. Find a possible value of P.

Nishimaster wrote:I worked it out just before you posted lol

how about this

when X^3 + pX^2 + p^2x - 36 is divided by x-3 the remainder is 21. Find a possible value of P.

Do long division and you get a remainder of 3[3(p+3) + p^2] - 36 = 21

Solve for p and you get -5 and 2