Question

what are the two values of x?(x+4)(x-6)=-21

Answer 1

Ok it might be worth multiply out and reformatting in to the quadratic form. \(ax^2+bx+c\)

Answer 2

Then you can plug it in to the quadratic formula to give the results.

Answer 3

with me so far?

Answer 4

ya the only thing is we got taught to do something different in my class

Answer 5

Ok, well you can do it graphically by drawing two lines on a graph. y=(x+4)(x-6) and y = 21. The points where these two lines intersect will give the answer. Is that the kind of thing you are looking for?

Answer 6

yeah im looking for a set of x values but we dont solve by graphing in this class either

Answer 7

its all algebraically with no quadratic formulas or graphing but im not sure what it is

Answer 8

Ok well a third and slightly harder to spot way of doing it is by completing the square. The idea here is get the equation in the form \((x-a)^2=b\)

Answer 9

that sounds more like what im supposed to do

Answer 10

So with our equation \((x+4)(x-6)=21\) we can multiply out.

Answer 11

...to give \(x^2-2x-24=21\) with me so far?

Answer 12

yes then its x^2-2x-3 which then is x^2-3x+x-3

Answer 13

or its x^2+x-3x-3 so its easier that way

Answer 14

then you factor them out x(x+1)-3(x+1)

Answer 15

(x+1)(x-3)

Answer 16

so -1,3?

Answer 17

Ok well we need to get the equation in the form \((x-a)^2=c\)
So just to continue on from \(x^2-2x-24=21\) we can add 24 to both sides which will give us ?

Answer 18

\(x^2-2x=45\) We can see that we are getting close to the form that we want it in right?

Answer 19

are the answers -1,3?

Answer 20

No

Answer 21

oh ok

Answer 22

So far we have \(x^2-2x=45\) with me so far?

Answer 23

yes

Answer 24

Great! so now we have to try and get \(x^2-2x\) in to the form \((x-a)^2\). So we need to find that value of \(a\). Because we have a \(2x\) we can safely say that a will be equal to \(1\). Giving us \((x-1)^2\). However if we expand that we get \(x^2-2x+1\) which is no quite what we want. Any questions on that so far?

Answer 25

not yet

Answer 26

Ok so to get rid of the \(+1\) we need to add1 from both sides.\[x^2-2x=45\]\[x^2-2x+1=46\]Remember from the above bit that \[(x-1)^2=x^2-2x+1\] which we now have!! Thus we can simplify our equation to \[(x-1)^2=46\]Does that all make sense?

Answer 27

it makes sense this is something that will take me a few times to remember, but yes continue

Answer 28

Yeah it's a bit hard to spot, but so far we have got to \[(x-1)^2=46\]We can simply square root both sides which gives us\[x-1 = \pm \sqrt{46}\]

Answer 29

ok i get this

Answer 30

Fantastic! Glad I could help

Answer 31

but whatsthe answer for x?

Answer 32

Ok well from\[x-1 = \pm \sqrt{46} \]It really shouldn't be too hard. Simply add 1 to both sides to give you the 2 solutions to x

Answer 33

What do you get?

Answer 34

not a whole number right?

Answer 35

\[x-1=+\sqrt{46}\]or\[x-1=-\sqrt{46}\]From there you can get the 2 values of x

Answer 36

thats difficult because I havnt done anything in this course yet where the answer wasnt a whole number or a very small fraction

Answer 37

Ok well the answer is simply written\[x=1+\sqrt{46}\]or\[ x=1-\sqrt{46}\] And that is the full answer. Hope that helps

Answer 38

ok thank you

Answer 39

WOOOAHAHAHHA

Answer 40

WAIT A SECOND!!!! I read the question wrong!

Answer 41

I thought it was (x+4)(x−6)=21 but actually the 21 is negative!!!

Answer 42

(x+4)(x−6)=-21

Answer 43

are you there?

Answer 44

Now I feel like an idiot of course you were right ages ago. I'm so sorry!!!

Answer 45

yeah my answer -1,3 was right haha

Answer 46

Yeah sorry buddy, my bad, read the question wrong, I feel like a wingspan. Sorry bro

Answer 47

its peerfectly ok you didnt know haha

Answer 48

i was like this person is crazy im goin with my answer haha

Answer 49

A great website for helping with that kind of maths is wolframalpha.com which is a great checking site.

Answer 50

Sorry again

Answer 51

thats ok and thanks for the site i think thats more of what im looking for