Algebra Help??

Question

can someone explain in detail how to do some of these problems??? its factoring...

5x(squared) - 15

100 - 36n(squared)

c(squared) + 14c +49

Answer 1

Look for common factors and patterns -

5x^2 - 15 = 5(x^2 - 3)

100 - 36n^2 = 4(25 - 9n^2) = 4(5 + 3n)(5 - 3n) This is a difference of squares pattern

c^2 - 14c + 49 = (c - 7)^2 This is a perfect square trinomial.

Answer 2

Alright well in the 5x(squared)-15 thing there is one thing common to both 15 and 5 that is 5 so you take that out and the answer is 5(x-3)

100 - 36n(squared) is a difference of two squares which means that both of the terms in the problem are squares ( 10 x10 is 100 and 6n x 6n is 36n(squared)) so you make the solution (10 +36n)(10- 36n)

Now this one is tricky c(squared) + 14c +49
For starters make two parentheses both starting with the variable(c) and plus signs because the terms are positve
(c+ )(c+ )
Now we must find two numbers that multiply to give you 49 and add to give you 14 they are 7 and 7
(c+ 7)(c+7)

Answer 3

i don't want to do everything for you, so i will just show you how to do the first.

5x^2-15

first, divide both sides by 5. you get x squared- 3. rearrange the equation so the 3 is on the other side.

x^2=3

now take the square root of both sides and you get x= plus or minus the square root of 3. now just use that as an example and try to do the rest yourself.

actually, for the third one you have to do something different.

c^2 + 14c+49

all you have to do is find two numbers that multiply to be 49 and add up to be 14. in this case it would be 7 and 7, so the answer is (c+7)(c+7) or (c+7)^2.

Answer 4

Well, 5x(squared) - 15 = 0, assuming that you forgot to put down what I have put down, which is the = 0,

By solving for x, we have to transfer -15 to the other side, by adding 15 to both sides which would still be true and equal, and it goes like this,
5x(squared) -15 + 15 = 0 + 15,
take note, (-15+15) = 0,
so we will have 5x(squared) = 15,
then by dividing both sides with 5, just as we add 15 but this time to separate the unknown from known.
And it goes like this, 5x(squared)/5 = 15/5,
and we will have; x(squared) = 3,
and by multiplying both side by x(to the power of 1/2),or square roots
we will have x = 1.732, or approximately at 1-3/4 which is the answer we seek.

Note; Just follow the system I have given you to solve the other remaining problems in sequences as I have presented. Good luck!!!

Answer 5

5x^2-15 can be written as 5(x^2-3) because it's still the same #, you basically just create more steps if you actually had to solve it. i don't know if that makes sense to you or if it's what you're looking for