Question

x^2+8x+4=0
solve the equation (choose the best method)

Answer 1

So what did you try?

Answer 2

i can do the equation i just wanna know what method and in my book is that but i left in school :(

Answer 3

When I look at \(x^2+8x+4=0\), the first thing I see is that they factors of 4 are either 1 and 4 or 2 and 2. There is no way those add up to 8. That means quadratic equation. Know that one?

Answer 4

yep thanks :)

Answer 5

Quadratic formula is the same as quadratic equation right

Answer 6

\(ax^2+bx+c\)
The relationship between \(a\cdot c\) and what adds up to b is what gives it away on these. When a is 1 it is not too hard.

Answer 7

Yah.

Answer 8

ok thanks

Answer 9

This cute little thing:\[\frac{-b\pm \sqrt{b^2-4ac}}{2a}\]

Answer 10

yep that's what i have

Answer 11

OK, then that is what you need here.

Answer 12

i'm gonna do it and i'm gonna give you my answer and u can check if its right

Answer 13

OK.

Answer 14

i got -0.26 and -7.74

Answer 15

Do they want aprox. or exact values? I did exact values.

Answer 16

sorry to bother you but what method is this one c^2-100=0

Answer 17

I think you got your root wrong n that last one. In approx. I get -.54 -7.46

Answer 18

exact

Answer 19

ok thanks

Answer 20

Exact means they will want it with the square root sign.

Answer 21

ok :) so sorry but can you give me the method of c^2-100=0

Answer 22

\[\frac{-8\pm \sqrt{8^2-4(1)(4)}}{2(1)} \implies \\

\frac{-8\pm \sqrt{64-16}}{2} \implies \\

\frac{-8\pm \sqrt{48}}{2} \implies \\

\frac{-8\pm 4\sqrt{3}}{2} \implies \\

-4\pm 2\sqrt{3}\]

As for the second one, look at 100. What is another way of saying 100 that uses an exponent? If you know that, you should know which method.

Answer 23

Recognize this form?\[c^2-100=0 \implies c^2-10^2=0\]

Answer 24

no i don't remeber can u give me the name of the method tho?

Answer 25

Difference of perfect squares

Answer 26

\(a^2-b^2=(a+b)(a-b)\)

Answer 27

oh like that i used another one

Answer 28

c-100

Answer 29

(c +100) (c-100)

Answer 30

You have to solve both the + and the - side, and it is the non-squared one you want. So not 100, 10.

Answer 31

Because \((10)(-10)=-100\)

Answer 32

so c-100 and c 100

Answer 33

i mean 10

Answer 34

Yes, \(c=\pm 10\)

Answer 35

Or in set notation, \(c=\{-10,10\}\)

Answer 36

i bother way to much but if you are free can u say me the the method of 2x^2-54=0

Answer 37

Well, 2 is not exactly a square... hmmm... neither is 54....

If you found some multiple in there that added up to 0, it might work...

54=9*6=3*3*3*2, so you might be able to just factor out the 2 and see if there is some other common factor in there...

Answer 38

I don't see that as one I would just say, "This method will work."

Answer 39

\[2x^2=54 \]

Answer 40

\[x^2=54\div2\]

Answer 41

\[\sqrt{49}\]

Answer 42

x\[x =\pm 7\]

Answer 43

the teacher taught us that one but idk if its correct

Answer 44

bye and thank :*

Answer 45

Well, the easist might be to factor the 2 and then just do difference of sqares, but then you are using a somewhat odd number for the b part. Still, it would work.

Answer 46

54/2=27

Answer 47

\[2x^2-54=0\implies \\

2(x^2-27)=0\implies \\

(x+\sqrt{27})(x-\sqrt{27})=0\implies \\
x=\pm\sqrt{27}
\]

Answer 48

Or with your teacher's way:
\[2x^2-54=0 \implies \\
2x^2=54 \implies \\
x^2=27 \implies \\
x=\sqrt{27}\implies \\
x=\pm 3\sqrt{3}\]

Which is the same thing.