x^2 - 49=0? How do you slove these!? Help!?

Question

Hey, can someone help me? It says I have to factor it and then slove them. I don't get it x^2 - 4x + 4= 0. I don't get this one either GRRRRRRRR! Can someone explain this to me and break it up thanks!

Answer 1

The Difference of two squares

x² - 49 = 0

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

- - - - - - - -

x² - 4x + 4 = 0

The middle term is - 4x

Find the sum of the middle term

x² = 1

Multiply the first term 1 times the last term 4 equals 4 and factor

Factors of 4

1 x 4
2 x 2. ..←. use these factors

- 2 and - 2 satisfy the sum of the middle term

Insert - 2x and - 2x into the equation

x² - 4x + 4 = 0

x² - 2x - 2x + 4 = 0

x(x - 2) - 2(x - 2) = 0

(x - 2)(x - 2) = 0

- - - - - - - - - -

Roots

x - 2 = 0

Transpose 2

x - 2 + 2 = 0 + 2

x = 2

- - - - - - - -s-

Answer 2

To factor the first one is simple, all you need to do is find two numbers that multiplied together gives you -49,

=> (x-7)(x+7)= 0 //Set each term equal to 0
=> x-7 = 0 and x+ 7= 0 // Solve for x
=> x= 7 (adding 7 to both sides) and x = -7 (subtracting 7 from both sides)

=> x = -7, 7 (answer)

Another way is to do it right from the equation you already have:

x^2 -49 = 0 // Add 49 to both sides
x^2 = 49 // To solve for x take the sqrt of both sides
sqrt(x^2) = (+-) sqrt (49) //Remember that sqrt is always positive or negative (+-)
x = (+-) 7
x = 7, -7 (answer)

Note that you would not be able to do this last method if you had a sum after the x^2 unless you are working with imaginary numbers

e.g. x^2 + 49
x^2 = -49
x = (+-) sqrt (-49) // does not exist in real numbers
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For the secon one is just as simple:

=> x^2 -4x +4 = 0
=> (x-2)(x-2) = 0 or (x-2)^2 //Again set each term equal to 0
=> x=2 (answer) // Adding 2 to both sides, it the same for both so you only need one.

Answer 3

You have to factor.

x^2 - 49 =0 can also be (x-7)(x+7) so x = -7,+7

x^2 - 4x + 4 = 0 can also be (x-2)(x-2) so x = 2

What you have to do is find factors of the last term that will add up to the middle term. The do FOIL to check your work.
So 7 is a factor of 49 ans since the middle term is zero you need negative and positive 7.

Answer 4

Well factoring is not so easy to learn at first. What you have to do is pretty much just punch in different numbers... sort of. OK,

x^2 - 49 = 0 factors out to (x+7)(x-7)=0, then you just solve...

x+7=0 or x-7=0
x = -7 or x = 7

S={-7,7}.

Now the second one...
x^2 - 4x + 4 = 0
(x-2)(x-2)=0
x-2 = 0 OR x-2 = 0
x = 2 OR x=2 which is the same thing, so there is only one solution
S={2}.

Sorry it is weird to explain. lol
Good luck!

Answer 5

the equation is the difference of perfect squares

use this formula
a^2 - b^2 = (a - b) (a + b)

x^2 - 49 = 0

x^2 - 7^2 = 0

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

set equal quanity equal to 0

x - 7 = 0
x = 7

x + 7 = 0
x = -7


so x = 7 or -7


x^2 - 4x + 4 = 0
(x - 2)^2 = 0
x = 2

Answer 6

Read your algebra book! It should have the answer to your first question. It'll look like this:
x^2 - a^2 = (x+a)(x-a)

Factoring the second one follows the more general form (you should know the Foil Method):
x^2 + (a+b)x + ab = 0 = (x+a)(x+b)

So, in your case,
(a+b) = -4 and ab = 4

So, what two numbers added together give you -4 and when multiplied together gives you 4?
Hint 1: they must have the same sign (both positive or both negative) because when you multiply them together they result in a positive number.
Hint 2: because they're the same sign (from Hint 1) they must be both negative because their sum is negative.

Yeah, that's all you get from me. It's your homework, right?

Answer 7

x^2 - 49 = 0
first add 49 to both sides.
x^2 = 49
next you need to find the roots of 49.
i do this by counting from one and going up till i find the numbers that i need to multiply.
1 * 49
2 * ? doesn't work
3* ? doesn't work
4* ? doesn't work
till i get something that does. in this case 7
7*7=49
then you notice you have two of the same numbers that is your square root.

x=7

hope that helps.

Answer 8

The difference of two squares:

x² & 7²

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

x = 7 or -7

Because if you substitute either one of these two values back into the original equation, the result will be zero.

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For the second one, just look at the result:

(x - 2) * (x - 2) = 0

x = 2 is the answer.

Answer 9

x^2 - 49=0
x^2 =49
x = 7
7^2=49 :)

x^2 - 4x + 4= 0
(x-2)(x-2)=0
(x - 2)^2=0
x=2

Answer 10

x^2-49 = 0
=>add 49 to both sides
x^2=49
=>take the sqrt of both side
x=7

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