Question

the product of 2 consecutive odd integers is 143. find the integers?

Answer 1

Let x be an odd integer.

Then, the next consecutive odd integer is x + 2.

Answer 2

The product of the two integers is the following:

x ( x + 2) = 143

Answer 3

@Garrett1234

Would you multiply this, please?

x ( x + 2) = 143

Answer 4

Use the distributive property to multiply x by (x + 2)

Answer 5

x^2 + 2x = 143 right? @Directrix

Answer 6

Yes.

Answer 7

Yes. Now bring the 143 over to the other side and solve the quadratic.

Answer 8

Now, it is time to factor x^2 +2x - 143 = 0.

Answer 9

Look for two numbers that multiply to -143 and add to +2.

Answer 10

@Garrett1234 What is ? below.

(x + 13) ( x - ? ) = 0

Answer 11

@Directrix How did you pull 13 "out of a hat"?

Answer 12

(x+13) (x-11) = 0 correct? @Directrix

Answer 13

@Garrett1234 Yes. So far, so good.

Answer 14

It is Zero Product Property time now.
If the product of two quantities is zero, then one or the other or both (the factors) = 0.

(x+13) (x-11) = 0
means

x + 13 = 0 OR x - 11 = 0

@Garrett1234 Would you solve each of those two equations for x?

Answer 15

\[(2 n+1) (2 n+3)=143 \]\[\{n\to -7,n\to 5\} \]{-13,-11} and {11,13}

Answer 16

@Garrett1234 Here's where left off:

(x+13) (x-11) = 0
means

x + 13 = 0 OR x - 11 = 0

@Garrett1234 Would you solve each of those two equations for x?

Answer 17

@skullpatrol @robtobey

Answer 18

So, x=-13, or 11 right?
@Directrix

Answer 19

Correct.

x + 13 = 0 OR x - 11 = 0

x = -13 OR x = 11
@Garrett1234

Answer 20

@Garrett1234 What is ? below?

If x = -13, then the next consecutive odd integer is -13 + 2 = ?

Answer 21

-11 right?
@Directrix

Answer 22

Correct, @Garrett1234

So, one answer pair is the integers: -13 and -11

But, there is another.

Answer 23

@Garrett1234 What is ? below.

If x = 11, then the next consecutive odd integer is 11 + 2 = ?

Answer 24

So the integers could either be -13, -11 or 11, 13 correct?
@Directrix

Answer 25

@Garrett1234

Yes, but remember that they come in pairs.
Avoid running them all together as 4 numbers.

The complete answer must have both pairs of integers:

-13 and -11 --> one pair AND

11 and 13 --> second pair

Answer 26

@Garrett1234

Questions?

Answer 27

No, you have been tons of help, thank you so much! You explained it all very clearly and took it step by step. @Directrix Although i do have one more problem that seems a little more advanced.

Answer 28

Glad to help. Post your next question in a new thread. We seem to have lots of Answerers interested in this work. That's great.

I will follow you to the new thread when you have the next question posted.
Okay?

@Garrett1234

Answer 29

Okay, and once again thanks! @Directrix

Answer 30

You are welcome.

I just saw that this is your first posted question in the mathematics section.

And, a BIG WELCOME to OPEN STUDY MATH.

If you have any questions about the site, just hit the @Directrix wherever you are working here. If I am online, I will find you and help.

Or, you can send a private message, and I will try my best to help out.

@Garrett1234

Answer 31

@aayush12345