stumped

[Sissy Devane]

The problem ask to solve, and give solutions

5x+x(x+2)=0
5x+x^2+2x=0
3x+x^2=0
x(x+3)=0
Now at this point I know I am suppose to solve for x, but I can't remember how to do this at this point....could I get a kick in the right direction please?

 

[mmm4444bot]

You're doing fine, except that you made an arithmetic mistake when combining the like-terms 5x and 2x.

5 + 2 does not equal 3.

After you fix this mistake, you'll have the correct factors. Next, set each factor equal to zero, and solve the resulting equations.

Do you have a textbook? If so, check the index to see whether or not you can find any information about something called the Zero Product Property.

This property is common sense. It says that if we get zero after multiplying factors together, then at least one or more of the factors themselves must also be zero.

(In other words, it's impossible to get zero by multiplying non-zero numbers together.)

Here's a simple example:

4x = 0

In order for the product of factors 4 and x to be zero, at least one of the factors MUST be zero. Obviously, 4 is not 0, so x must be zero.

We can show that x is zero by solving the equation. Divide both sides by 4.

(4x)/4 = 0/4

x = 0

Here's another example:

(x + 2)*(x - 3) = 0

The two factors are x + 2 and x - 3.

The equation indicates that the result of multiplying these factors together (i..e, their product) is zero.

Therefore, the Zero Product Property tells us that one or both of these two factors MUST be zero.

So, we set each factor equal to zero; this gives us two equations.

x + 2 = 0

x - 3 = 0

Solving these two equations gives us the values of x that are solutions to the original equation.

In your exercise, set each factor equal to zero, and then solve those equations. (Of course, the equation x = 0 does not need to be solved; it's already "solved").

Thank you for showing your work. It really helps tutors when students show what they're thinking.

 

[Sissy Devane]

Yes I posted it wrong, but this is what I have
x(x+3)=0

the first one is
x=0
the second is
x+3=0
x+3-3=0-3
x=-3

Then I but the answers 0 and -3 back into the orginal equation to check the solutions
5x+x(x-2)=0
5*0+0(0-2)=0
-2 does not equal 0

5*-3 +[-3(-3-2)]=0
-15+(9+6)=o
-15 + 15=0
0=0 this is a solution

so -3 is the only solution for this?
the x intercepts would be (0,-3) is this correct?

 

[Mrspi]

Yes I posted it wrong, but this is what I have
x(x+3)=0

the first one is
x=0
the second is
x+3=0
x+3-3=0-3
x=-3

Then I but the answers 0 and -3 back into the orginal equation to check the solutions
5x+x(x-2)=0
5*0+0(0-2)=0
-2 does not equal 0

5*-3 +[-3(-3-2)]=0
-15+(9+6)=o
-15 + 15=0
0=0 this is a solution

so -3 is the only solution for this?
the x intercepts would be (0,-3) is this correct?

I guess you did not pay attention to the previous post.....
You had

5x + x(x + 2) = 0

Do the multiplication to get rid of the parentheses:

5x + x[sup:32v3bou5]2[/sup:32v3bou5] + 2x = 0

Then combine like terms. Did you not see the previous response which reminded you that 5x + 2x is NOT 3x???? I guess you didn't.

Since you persisted in thinking that 5x + x[sup:32v3bou5]2[/sup:32v3bou5] + 2x is x[sup:32v3bou5]2[/sup:32v3bou5] + 3x, it is not surprising that your answers did not check.

 

[Sissy Devane]

I also stated I posted the equation wrong but in my response I gave the correct equation of
5x+x(x-2)=0
that is why I came out with I came out with 3x
therefore I have
I ended up with
x(x+3)=0
x=0 and x=-3
But I see were I went wrong now,There is no need to be ugly about this, some people can make mistakes.....

 

[mmm4444bot]

Yes I posted it wrong, but this is what I have
x(x+3)=0

Sorry, this correction is not good enough. You've used an unreferenced pronoun; your statement above does not make clear what you did wrong, such that we can be confident of whatever it is with which you started. I read the phrase, "but this is what I have" to mean "trust me, I know what I'm doing, up to this point".

No can do, Sissy D.

Mathematics is sufficiently precise as to require clear corrections of misinformation before continuing. Anything less remains cloudy.

'

… the x intercepts would be (0,-3) is this correct?

Yes, the numbers are correct, but they're confusing, the way that you typed them.

Whenever you list a set of numbers, use curly braces instead of parentheses. Use of parentheses indicates something else, with a pair of numbers.

The x-intercepts are written {-3, 0}, if you don't want to write their coordinates.

We use parentheses to write an ordered pair of numbers. With respect to points in the xy-plane (eg: x-intercepts), these ordered pairs are the (x,y) coordinates of the points' locations.

So, we could also write the x-intercepts in terms of their coordinates (the preferred way, for me):

(-3, 0) and (0, 0)

PS: There's a Preview button next to the Submit button. I use it often to proofread my posts before clicking Submit.