Question

x2 - 49 = 0 (factoring) Need help not answers

Answer 1

x2=49
x=7,x=-7

Answer 2

how do you get that though? >.<

Answer 3

(x-7)(x+7)=0
x=7,x=-7

Answer 4

just look at the second way since you said by factoring

Answer 5

but it doesnt add to -49 that way?

Answer 6

if you have a^2-b^2,
then the factors are (a-b) and (a+b)

Answer 7

what do you mean?

Answer 8

since the 2 terms are a difference of 2 squares, you can use:

\[ (x^2 - y^2) \]
\[ (x + y)(x - y) \]

Answer 9

oh

Answer 10

Use that as your guide.

Answer 11

what if they go like x2 + 24 = 10x?

Answer 12

Move 10x to the other side and use the quadratic equation :

\[ ax^2 + bx + c = 0 \]

Answer 13

and solve by getting x2 + (add) = (multiply) like as in x2 +16x +48)?

Answer 14

?

Answer 15

x^2+24=10x
x^2+24-10x=10x-10x
x^2-10x+24=0
(x-6)(x-4)=0

Answer 16

if you have x^2+bx+c=0
just find factors of c that add up to be b
if you cannot then you cannot factor over the integers

Answer 17

Then you can use 3 methods in solving for the roots of x.

First, by factoring.
example:
\[ x^2 -4x + 3 = 0 \]
\[ (x - 3)(x - 1) = 0 \]

Second, by completing the square.
example:
\[ x^2 -4x = 5\] Find a term that will make the equation a perfect square trinomial the add the term on both sides
\[ x^2 -4x +3 = 5 + 3 \]
\[ x^2 -4x +3 = 8 \]

Third, by using the quadratic equation.

\[x = -b \pm \sqrt{b^2 - 4ac}\]------------------ \[ 2a \]

Answer 18

k
now to the next 2x^2 - x - 6

Answer 19

But i prefer to use factoring because it's the easiest. :)

Answer 20

if you have ax^2+bx+c
find two factors of a*c that add up to be b
so we have 2x^2-x-6
so a=2,b=-1,c=-6
a*c=2(-6)=-4(3)
and
-4+3=-1(=b)
so we replace -x with -4x+3x
and then factor by grouping

Answer 21

2x^2-4x+3x-6
2x(x-2)+3(x-2)
(x-2)(2x+3)

Answer 22

but the (x)?

Answer 23

In getting the x, since the starting equation is equated to 0, then equate both factors to 0.

Answer 24

x - 2 = 0 and 2x + 3 = 0

There you can solve the 2 values of x

Answer 25

btw before x2 + 24 = 10x? if the middle contains an x? doesnt it show?

Answer 26

x2 -10x + 24?

Answer 27

Yes. Using APE, you will have

\[ x^2 + 24 -10x = 10x - 10x \]

to eliminate x

that leads to

\[ x^2 + 24 - 10x \] or \[ x^2 -10x + 24 \]

Answer 28

to move the 10x i mean.

Answer 29

with myin though its gone?

Answer 30

x^2+24=10x
x^2+24-10x=10x-10x
x^2-10x+24=0
(x-6)(x-4)=0

shoudnt their be an x on the last line

Answer 31

What last line? the very answer? He didn't show the whole solution. he just showed you a part of it for you to work alone.

Answer 32

she*

Answer 33

well give me another example with an x in the middle and show me the steps through it?

Answer 34

If you're going to continue that' we'll have:

x^2+24=10x
x^2+24-10x=10x-10x
x^2-10x+24=0
(x-6)(x-4)=0

x - 6 = 0 ; x - 4 = 0
x = 6 ; x = 4

Answer 35

Sorry. lol. :)

Answer 36

yea i know that but theirs 3 x's

Answer 37

x^2+24=10x <=== Wheres the ten's x gone?

Answer 38

What do you mean?

Answer 39

the x should not disappear?

Answer 40

The term with the x will not disapper, it will just be moved to the other side to for the basic quadratic equation ax^2 + bx + c = 0

Answer 41

disappear.

Answer 42

x^2-10x+24=0
(x-6)(x-4)=0
the ten's x is not there shouldent it have been like
X (x-6) (x-4) or (x2-6) (x-4)?

Answer 43

im very confused?

Answer 44

No. It's hard to explain but try to do the FOIL method to check that the factor is right.

Answer 45

ok do you believe that -10x=-6x-4x?

Answer 46

yes?

Answer 47

yes

Answer 48

ok
we have
x^2-6x-4x+24=0

Answer 49

factor by grouping
what do the first two terms have in common

Answer 50

just look at x^2-6x right now
what factors do x^2 and 6x share?

Answer 51

x?

Answer 52

thats right!
so we can do
x(x-6)-4x+24=0
right?

Answer 53

yes also did i do 4x2 -10x right with the answer of (2x - 5)?

Answer 54

ok what do -4x and 24 have in common?

Answer 55

That's a different case.

Answer 56

i dont want to sound stupid but #'s?

Answer 57

what is but #s?

Answer 58

12 ? 4?

Answer 59

To factor that, you have to get the common factor of each. 4x^2 and -10x have a common factor of 2x so we do it like this : 2x(2x - 5)

Answer 60

ok i dont know what you are talking about just go with me for second
we have
x(x-6)-4x+24=0
this is getting somewhere
now what factors do 4x and 24 have in common?

Answer 61

http://www.gradeamathhelp.com/how-to-factor-polynomials.html

Answer 62

I have to go now. See you guys.

Answer 63

:(

Answer 64

thank you both

Answer 65

hey we aren't done lol
what do 4x and 24 have in common?

Answer 66

come on derp you can do it

Answer 67

im done? lol i need help with area now i give up >.>

Answer 68

(x^2)-49=0
If you have two quantities that are the square of a number being subtracted and equal to 0, then (a+b)(a-b)=(a^2)-(b^2).
This general formula will help as you do more problems and get the feel for factoring. It is also helpful to memorize the squares of numbers 1-12 for basic factoring problems. They usually don't get higher than that.
In this case, you can say that (a^2)=(x^2), therefore a=x and (b^2)=49. You can find the value of b by taking the square root of each side, to isolate the b from any variables. When you do this, you get b=sqrt49, or b=7.

So, put this into the general formula and you get
(x+7)(x-7)=0.
So, your factors are
(x+7) and (x-7)

If you need to solve for x, then you set each factor equal to 0 (as stated in the equation) and simply solve it like you would any other algebraic equation.