Question

Will fan and medal!!

Two consecutive negative integers have a product of 30. What are the integers?

Separate the answers with a comma

Answer 1

Represent the integers. Let x be the first integer. If these negative integers are consecutive, then how would you represent the next one?

Next, how would you represent the PRODUCT of these two unknown negative integers?

Answer 2

I have no clue how to do that... x-x^2?

Answer 3

Slow down a bit. Let the first negative integer be x.
What's the next larger integer?

Answer 4

Represent the unknown quantities before you try to use these representations in an equation.

Answer 5

Hint: What does "consecutive" mean?

If I were to give you the integer 7, what would the next consecutive integer be?

Answer 6

8would be the next one?

Answer 7

That's right! "consecutive" in this case means "separated by 1."

Answer 8

So, if the given integer were 7, the next consecutive integer would be 7+1 = 8. So you are right.

Answer 9

Not every problem needs to be solved with an equation.
The problem is not asking specifically for an equation.
Think of the factors of 30.
Can you think of two consecutive numbers that are factors of 30 whose product is 30?
Since the product is positive, and you are looking for 2 negative numbers, just make the two factors above negative.

Answer 10

Now suppose the first integer is x.
What is the next consecutive integer? Write it algebraically, since we don't have a value for x.

Answer 11

y? @mathmale and I'm not good with factors @mathstudent55

Answer 12

You were right before. I gave you the integer 7 and asked for the next consec. int.
You added 1 to 7 and got 8. That's correct.

Now the first integer is 7. What is the next consec. int.?

Answer 13

8?

Answer 14

Examples of consecutive integers: 2, 3, 4, 5, 6, ...
Examples of consecutive even integers: 2, 4, 6, 8, ...

Answer 15

Yes. Sorry for being repetitive.
I give you x as the first integer.
How do you represent the next consecutive integer? (See my examples, above.)

Answer 16

Example: first integer is 9. Next consec. int. is 9+1=10.
Problem: first integer is x. Next consec. int. is ..... ????

Answer 17

I don't know, all i can think of is y comes nextand you saidno ;-;

Answer 18

Lets make it easy for you..
when you multiply two negative numbers u are gonna get a positive one, so the only thing that u need to do is find two numbers that are consecutive, i mean, one is behind the other and when u multiply them u get 30

Answer 19

@papiernesto: I'd suggest you work on the concept of "consecutive integer" first.

Answer 20

I'm getting really confused...

Answer 21

@WhatEven: I'm sorry you're feeling confused. Rather than continue to explain, I'm going to ask you to ask questions here whose answers will get you on the right track.

Your difficulty seems to lie in understanding the concept of "consecutive." Have you tried looking that up online?

Answer 22

@WhatEven
This is what @mathmale is trying to tell you:

integer 5, next consecutive integer is 5 + 1 = 6
integer 7, next consecutive integer is 7 + 1 = 8
integer 20, next consecutive integer is 20 + 1 = 21

For all the integers above, 5, 7, 20, to find the next consecutive integer you add 1.

If the integer is x, what do you do to it to find the next consecutive integer?

Answer 23

The word "consecutive" means the "next one."
Consecutive integers means integers that follow each other.
Since the integers are the whole numbers, including the negative whole numbers, if you have an integer, the next consecutive integer means the next integer.

Answer 24

Y! the nextone would be y! like x, y z.

Answer 25

Y is the only thing nthat makes sense to me

Answer 26

I didn't ask yet what the next consecutive integer after x is.
I'm doing it a small step at a time.

Answer 27

We saw above that for any integer you have, the next consecutive integer is obtained by simply adding 1.

Answer 28

so x^2? ;-;

Answer 29

using additional variables just makes the problem harder.
This is an algebra course. In algebra we learn how to represent quantities with letters instead of with specific numbers. If x is the first integer, then the next consecutive integer is x+1, exactly as mathstudent55 has explained.

Answer 30

The next consecutive integer to 5 is 6.
The next consecutive integer to 100 is 101.
You always add 1 to an integer to get the next consecutive integer.

Answer 31

So, if the first integer is x, @WhatEven, please add 1 to x to get the next consec. int.

Answer 32

If the integer we are dealing with is called x, then what do you do to it to get the next one?
Hint: you do the same as from 5 to 6 , or from 20 to 21 or from 100 to 101.

Answer 33

First integer: x
Second integer: (you fill this in, please)

Answer 34

I just said x^2 above..

Answer 35

You are using exponentiation. That doesn't belong in a discussion of consecutive integers.

First integer is x.
Add 1 to that (as mathstudent55 has explained) to get the next integer: it is x+1.

So, we represent these 2 consec. integers by x and x+1.

Answer 36

Question: What operation do you do to 5 to get 6?
Answer: You add 1

Question: what operation do you do to x to get the next consecutive integer?
Answer: you add 1 to x

Integer: x
Next consecutive integer: 1 added to x.
Can you write "1 added to x" using mathematical symbols, such as 1, x, +?

Answer 37

x+(x+1) ?

Answer 38

Forming a product requires that we multiply two quantities together. 6*7 is a product, and the product is 42.

Write, symbolically, the product of x and (x+1).

Answer 39

Integer: x
Next consecutive integer: x + 1

Answer 40

Your x + (x+1) is not a product; it's a sum.

Answer 41

But you're on the way. Try again, please.

Answer 42

so x(x+1)

Answer 43

\(\LARGE \color{red}{BINGO!} \)

Answer 44

The product of x and (x+1) is .... YES, you've got it.
The problem states that the product of these two integers is 30.
Write an equation showing this fact.

Answer 45

and wail wouldn't it be -x(-x+1) ?

Answer 46

Your x(x+1) is the product in question and is correct.
This product is equal to 30.
Write the equation, please, using an ' = ' sign.

Answer 47

30=-x(-x+1)
or
30=x(x+1)

Answer 48

Only the 2nd one is correct. You will see why, later.

Answer 49

That's what I asked and you toldme to put 30 and an = ._.,

Answer 50

Now your job is to find the value of x that satisfies the problem statement. What do you do next? x(x+1)=30

Answer 51

Hint: multiply out the left side of this equation.

Answer 52

-5 and -6?

Answer 53

You are jumping ahead. Please go through all of the algebra needed to solve this problem.
If x(x+1)=30, multiply out the left side of the equation.

Answer 54

Hint: use the distributive property of multiplication.

Answer 55

I don'tknowwhat to multiply by what..

Answer 56

Multiply (x+1) by x. Use the distributive property of multiplication.

Answer 57

Example: z(q+1)=zq+z

Answer 58

x^2+x

Answer 59

very nice.
then x(x+1)=30 becomes

x^2 + x = 30

Answer 60

How would you solve this quadratic equation?

Answer 61

Hint: re-write it, in the form ax^2 + bx + c = 0

Answer 62

Move the 30 to the left side of our equation, replacing it with 0 on the right side.

Answer 63

so 30/x^2?

Answer 64

You have x^2 + x - 30 = 0 (after having moved 30 to the left side).

Answer 65

Your next task is to SOLVE this quadratic equation for x. How would you do that?

Answer 66

I think factoring would be the fastest method.

Answer 67

30.x^2?

Answer 68

WhatEven: those are not factors.

Think back to factoring quadratics. x^2 - 2x + 1 factors to (x-1)(x-1).

Your x^2 -x - 30 factors to what? give the two factors, please.

Answer 69

I don't know that;s the whole reason i came here, I feel like you're asking me to pull a number out of thin air and it;s extremely frustrating,.

Answer 70

I am very sorry you are frustrated. I am working on helping you develop the necessary skills to solve these math problems by yourself. When you have done well, I have told you so. When you have not done well, I've given you hints and asked you questions. You have studied the factoring of quadratics before, so this is just an application of something that should be familiar.

Answer 71

I don;t know how to factor it though, I am sorry if I sound as if I'm being rude I'm just tired and trying to finish this assignment and I'm not good at this. I can barely even multiply without a calculator and I always feel like algebra pulls numbers out of thin air, I need to know why and how you do or get something, I was trying to let you know so you don't waste time explaining something that's making me want to cry because it looks like mumbo jumbo

Answer 72

Do you have an algebra book with you that shows examples of the factoring of quadratic equations?

Answer 73

No

Answer 74

The topic here is "factoring quadratics." Have you ever tried searching the Internet for explanations of concepts that are difficult for you?

Answer 75

Yes I have it doesn't make sense tome as I said that;s the whole reason I came to open study

Answer 76

I know you must feel you are running out of time and growing more frustrated by the moment, but perhaps a video discussing this topic would help. One such video is

https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/factoring-quadratic-expressions-core-algebra/v/factoring-quadratic-expressions

Answer 77

Factoring x^2 - x - 30:

If a quadratic of this kind can be factored, the factors will look like (x - a)(x + b).

Without explaining why yet, I'll ask you to find possible factors of -30. For example, 2 and -15 are factors of -30, and (2)(-15) = -30.

Answer 78

5 and -6 are also factors. -5 and 6 are also. Are you with me this far?

Answer 79

Iam

Answer 80

Also ifI gooffline my comp has died

Answer 81

Ok. Let's take the two possible factors 5 and -6 of -30 and form possible factors of x^2 - x - 30 from them: 5 translates into the factor (x - 5) and -6 translates into the factor (x + 6).

We now have to multiply these possible factors together to determine if they are correct.

Answer 82

(x-5)(x+6) is multiplied using the FOIL method. We get x^2 + 6x -5x -30.

Answer 83

Is this the same as x^2 - x - 30? yes or no

Answer 84

no

Answer 85

theyboth need to be -

Answer 86

That's correct. So our tentative factors (x-5) and (x+6) are wrong.
Let's re-write them as (x+5) and (x-6). Multiply these together, please. Use the FOIL method.

Answer 87

Stillwrong. it needs to be (x-5) (x-6)

Answer 88

Not so. I was asking you to MULTIPLY these 2 factors.
(x+5)(x-6) = x^2 - x - 30, which is correct.

Answer 89

Whoops,sprry, I must've typedit in my calc wrong

Answer 90

Forgive me for saying this, but you might be better off using the calculator ONLY to check answers. Do the problems in your head or on paper. Otherwise the calculator gets to be a crutch.

Answer 91

So we have just about solved this problem.

x^2 - x - 30 = 0 becomes (x+5)(x-6) = 0. What 2 x-values satisfy this equation?

Answer 92

Hint: set each factor = to zero separately and solve each of the resulting 2 equations.
(x+5)=0 results in x = ?

Answer 93

(x+5)=0 is the same as x + 5 = 0.
Subtract 5 from both sides of the equation to solve it for x.

x+5-5 = 0 - 5, or x = -5. OK with that?

Answer 94

I'm sorry you were apparently so frustrated that you logged off OpenStudy. We had both invested a lot of time and thought into solving this math problem, and were minutes from obtaining the correct solution.

x^2 + x = 30 translates into x^2 + x - 30 = 0.
The factors of the left side are (x + 6) and (x - 5).
Setting x + 6 = 0, we get x = -6. Setting x - 5 = 0, we get x = 5. Discard x = 5, because we need two consecutive NEGATIVE values for x.

Then the first negative integer is x = -6. The second is x + 1 = -6 + 1, or -5.

Are these consecutive negative integers? Are -6 and -5 consecutive neg. ints.? YES.

Does their product equal 30? (-6)(-5) = 30? YES.

The solutions to this problem are thus {-6, -5}.