Question

544x=425eight find the base x

Answer 1

Thanks Ranga for helping me out again

Answer 2

First convert 425 base 8 to decimal

Remember the way we converted various base numbers to the decimal system before.
Do the same here.

To convert a three digit number say ABC base 8 to decimal, we do the following:
C + B(8^1) + A(8^2)

Can you convert 425 base 8 to decimal and tell me what you get?

Answer 3

ok give me a sec here

Answer 4

651?

Answer 5

I think my brain is fried been doing these problems for 3 days

Answer 6

Try again. Let me show it clearly by using the Equation button below the reply box. Give me a second.

Answer 7

ok

Answer 8

\[425_{8} = 5 + (2)(8^{1}) + (4)8^{2} = ?\]

Answer 9

now do i times the 8 x2 or add them?

Answer 10

83?

Answer 11

you do 2 times 8
then you do 4 times 8 times 8
then you add all three numbers

Answer 12

ok just sec

Answer 13

267

Answer 14

close but not quite

Answer 15

did I just do my math wrong? did it 3 times now?

Answer 16

2 x 8 = ?

Answer 17

16

Answer 18

ok.
4 x 8 x 8 = ?

Answer 19

256 which I got those 2

Answer 20

5 + 16 + 256 = ?

Answer 21

OH I see what I did duh....277

Answer 22

OK.
Now on the left you have 544 base x. Don't let the x throw you off.
Follow the same rule as before to convert it to decimal.

Answer 23

\[544_{x} = 4 + (4)(x ^{1}) + (5)(x ^{2}) = 5x ^{2} + 4x + 4\]

Answer 24

ok just sec

Answer 25

I have given you the answer above about how to convert base x to decimal. Go through it and see if it is clear or ask me if you have doubts.

Answer 26

yes I do have doubts about adding the x's together I know dont let it throw me off but it does

Answer 27

5x(little2) =4x=4 does throw me off

Answer 28

I meant + where there is =

Answer 29

544 base x
The last term 4 stays as 4.
The next term to the left is also a 4 but it has to be multiplied by x (which is the base) raised to 1. So it will be 4x^1 = 4x
The next term to the left is 5 and that has to be multiplied by x^2 so that will be 5x^2

Add them up and you have 5x^2 + 4x + 4

Answer 30

ok so the little triangle thingy is divide

Answer 31

oh no i understand k give me asec

Answer 32

now once you have 5xsquared+4x+4 what do you do with the 4?? this is where Im getting all kinds of confused

Answer 33

the little triangle thingy denotes exponent.

Since superscripts are not easy on a keyboard we use that ^ instead

x^2 =
\[x ^{2}\]

Answer 34

Yes gotcha

Answer 35

OK. Now remember the problem. We converted the left hand side to decimal and we converted the right hand side to decimal. Now just set them equal.

Answer 36

\[5x ^{2} + 4x + 4 = 277\]

Answer 37

yes ok so we put it together now

Answer 38

Subtract 277 from both sides:

Answer 39

k

Answer 40

\[5x ^{2} + 4x - 273 = 0\]

Answer 41

YES i got that far thats where I am stuck since you cant combine x's so do I bring the 4x over???

Answer 42

No. This is called a quadratic equation and there is a formula to find the values of x.
Do you know the formula?

Answer 43

No I wish I did!!!

Answer 44

I should know it but I dont remember it

Answer 45

oh, you have to look up the formula and become familiar with solving quadratic equations.
You will come across it a lot in algebra.

Answer 46

yes see I was having problems in Algebra so I switched over to Liberal Arts Math and yeah this is not any better plus the book is online and does not go into detail on helping our professor encourages us to search the internet for answers and this does not help me at all..someone that struggles as it is you know what I mean...its a online course if you havent guessed

Answer 47

If the quadratic equation is
\[ax ^{2} + bx + c = 0\]
then
\[x = \frac{ -b \pm \sqrt{b ^{2} - 4ac} }{ 2a }\]

So to solve any quadratic equation simply compare the general formula with the equation you are trying to solve and find what a, b and c are.

Answer 48

Oh goodness

Answer 49

no wonder Im lost

Answer 50

The general quadratic equation is:
\[ax ^{2} + bx + c = 0\]
The equation that we are trying to solve is:
\[5x ^{2} + 4x - 273 = 0\]
Compare them term by term and you will recognize
a = 5
b = 4
c = -273

Follow?

Answer 51

is it 6? yes I filled them in sorry I should tell you what Im doing :) Yes I filled them in...

Answer 52

I am getting slightly different answer.
First calculate b^2 - 4ac that is inside the square root.
a = 5, b = 4, c = -273
4^2 - (4)(5)(-273)
16 + (4)(5)(273)
16 + 5460
5476

Follow

Answer 53

oH im getting so frustrated worked it like 5 times... ok let me try again

Answer 54

ok yes then you divide 5476 divided by 10 right?? 2(a) is 10???

Answer 55

I was actually doing it right!!!!! what you did up top is what I have on my paper

Answer 56

no its not divided by 10 sorry

Answer 57

First you have to take the square root of 5476

Answer 58

2,378??

Answer 59

No, square root of 5476 = 74 (you have to use a calculator or you can use Google calculator)

Answer 60

NO 74

Answer 61

Oh yeah thats what I put LOl

Answer 62

then I divide by the 2(a) right

Answer 63

or is it 10 or 12?? divided into 74 trying to figure

Answer 64

Not yet. A quadratic equation has two solutions.
The plus/minus sign you see in the formula means first you have to take it as a plus sign and find x and then you have to take it as a minus sign and find x two get two values for x.

\[x = \frac{ -4 \pm 73 }{ (2)(5) } = \frac{ -4 + 73 }{ 10 } or \frac{ -4 - 73}{ 10 }\]

Answer 65

OH THATS what I did wrong! so which do you use?

Answer 66

OOps. It should be 74 not 73.

Answer 67

no I got it

Answer 68

\[x = \frac{ -4 + 74 }{ 10} or \frac{ -4 - 74 }{ 10 }\]

Answer 69

right ...so now I ask which one do I do and when I did both I dont get a even number?? and I have to have a even number for the answer

Answer 70

In this problem you can ignore the second solution because it gives a negative value and for problems involving bases a negative number is not used.
So we will use the first solution.
-4 + 74 = 70 and when it is divided by 10 you get 7.

So x = 7

Answer 71

OH ok so you want the positive solution then... OH I UNDERSTAND!!!!!! wow that is something that is way over my head!!!!!!!!!!!!!! I have to get some tutoring for all this!!!!!

Answer 72

Quadratic equations and their solutions keep cropping up in Algebra and so it is better to get some practice solving quadratic equations. Also you have to remember the formula for x I gave earlier.

Answer 73

Right..... yes I agree I need more of these to practice and yes they do pop up I remember some way back in High School geez but have totally slipped my mind now.... I need some extra help.... I sure so appreciate yours!!!!

Answer 74

Your awesome with math wish I was gifted that way! :)

Answer 75

People have different gifts. There are probably certain things you excel in thatothers dont.

So good luck.

Answer 76

Very true!!! I appreciate it very much and hope you have a wonderful night!!! :)

Answer 77

You too. Bye!

Answer 78

Bye :)