Question

Will someone please tell me what you do, step by step to solve a quadratic equation. I am having trouble specifically with the discriminant, and with completing the equation for the solutions. I have the formula memorized, so no problem there.

Answer 1

I'm not sure what you mean. If you have the formula, at which point do you get stuck?

Like, where do you get stuck trying to find the zeroes of:
\[x ^{2} - x + 1\]

Answer 2

Here is an example: \[x^2 -4.4x +2.8=0\] i can get all the way to finding the discriminant, but i have no idea how to find the solution after that.

Answer 3

i am sitting at \[x= 4.4 + \sqrt{43.008} \] and \[x= 4.4-\sqrt{43.008}\] both divided by two

Answer 4

You made a mistake under the root. The formula at that point is

\[\sqrt{b ^{2}-4ac}\]

Answer 5

b in this case being -4.4, a =1 and c = 2.8

Answer 6

which comes out to be 8.16

Answer 7

Yes.

Answer 8

i still do not know what to do with it after this point

Answer 9

There is not much you can do, without a calculator, I don't think they want you to solve the root of 8.16 by hand

Answer 10

i see the error by the way, thank you for pointing that out

Answer 11

No problem, the results of x at y=0 are then

x=\[4.4+\sqrt{8.16}\over2\] and x=\[4.4-\sqrt{8.16}\over2\]

Answer 12

it doesn't simplify further?

Answer 13

you can make that prettier when you divide 4.4 by 2 and take 1/2 into the root which then becoms 1/4 and divide 8.16 by four. But that's it. Unless you are allowed to use a calculator and take the root of 8.16

Answer 14

Need the working?

Answer 15

yes please

Answer 16

it needs to be simplified

Answer 17

Ok, so you can write the fracture into:

\[4.4\div2 + \sqrt{8.16}\div2\]

Answer 18

so: \[2.2 + \sqrt{4.08}\] and \[2.2-\sqrt{4.08}\] both being divided by 2

Answer 19

Then you can square 2 which gives four and put in under a root (then it would be two again, but you leave it at that. Then you when its division or multiplication, you are allowed to divide first, then take the root. This gives:

\[2.2 + \sqrt{8.16 \over 4}\]

Answer 20

Yes, you did this right!

Answer 21

Oh, no sorry, too quick! You forgot one step. You cannot change the value of 2 in this equation, so under the root it becomes four!! That is important. Do you understand?

Answer 22

the answer is 3.63, 0.77 but how in the world did they get that?

Answer 23

Well, with a calculator you can just type in root of 2.04, and add it to 2.2 for the first x and subtract it to get the second.

Answer 24

This gives you the numbers in the answers.

Answer 25

the root of 2.04?

Answer 26

Yes, 8.16 divided by four gives 2.04.

Answer 27

ok, how did you know to divide it by 4?

Answer 28

Ok, so in the equation it says \[\sqrt{8.16}\over2 \] are you with me?

Answer 29

so far

Answer 30

Now, it doesn't matter wether you take the root of 8.16 and divide it by two or you can do it the other way around. This is one of the fundamental arithmetical laws of mathematics:

The equasion can be rewritten to\[\sqrt{8.16} \times {1\over2}\]

Answer 31

Still with me?

Answer 32

lol, not sure if i am now

Answer 33

Dividing by two is the same as multiplying by one half, never heard of that?

Answer 34

yes that makes sense

Answer 35

OK, that is the only thing I have done so far.

Answer 36

Now, you can do whatever you want with one half, as long as it stays one half technicaly. For example you can make it 2/4 or 30/60, it doesn't matter to the outcome of the equation, are you following?

Answer 37

yes

Answer 38

Great! So why don't we say we don't say one half, we say \[{1\over \sqrt{4}} = \sqrt{1\over4} = {1\over2}\]] because that is the same as one half, right?

Answer 39

Following?

Answer 40

yes I believe so

Answer 41

Ok, so now we rewrite the equation to

\[\sqrt{8.16}\times \sqrt{1\over4}\]

Ok?

Answer 42

Now, it is laws of mathematics we apply: Because under the laws of arithmetic if the operation is divison or multiplication, we can perform these tasks BEFORE we take their roots. So we can rewrite to:

\[\sqrt{8.16\times{1\over4}} = \sqrt{8.16\over4}\]

Answer 43

And there we go, this equals:

\[\sqrt{2.04}\] which is as far as we can simplify without using a calculator.

Answer 44

that makes sense

Answer 45

so i could divide by 4 even if the number was 9.69?

Answer 46

Yes of course, as you saw, the four comes solely from one half, it has not anything to do with the other number.

Answer 47

But I can ask you this: if you were supposed to divide by three in the beginning, what would you have to divide by then under the root?

Answer 48

my guess would be 6

Answer 49

no, what does a root do? it finds the quadratic exponent of the number so you to get the same result as before you have to square the number. So three squared would be?

Answer 50

9

Answer 51

yes! to take the divisor three under the root, you would have to square it, and thus divide by nine in the root.

Answer 52

ok. i understand now, after you do that, what are the operations to complete the solution?

Answer 53

Well, you simply do what the equation says, in the case above, you divide 8.16 by four, take its root and subtract it from 2.02

Answer 54

if you are not allowed to use a calculator, simply write 2.02 ± root of (2.04)

Answer 55

im allowed to use a calculator

Answer 56

Well there you go, then take the root of 2.04 and add it to 2.02 for the first x, and subtract it to get the second x

Answer 57

There are always two results for a quadratic equation.

Answer 58

im not sure how to get the root with the calculator though, i a using windows 7 calculator, scientific view

Answer 59

is it 1.42?

Answer 60

puh, well i think you have to type in the number, and press the root symbol, did it work?
should give: 1.42....

Answer 61

yes, thats what the calculator said? well technically it is 4.3 because it's 1.428... so you have to round up to 1.43

Answer 62

sorry, 1.43

Answer 63

Alright, is everything clear so far? I have to leave now, hope I could help a little.

Answer 64

it's giving me 1.418

Answer 65

you have been abig help thank you

Answer 66

no worries! take care