'Solve 16x=x^2': What sort of question is this?

[jhawk555]

Can someone please direct me in the right direction. I am trying to review what I've learned and I ran into a problem where I don't know where to begin. I am not looking for the answer by any means, just a little nudge.

. . .Solve 16x = x^2

What type of problem is this? I know it isn't graphing. I was thinking that maybe it should go into standard form. x^2 - 16x = 0 and then solve for x by completing the square.

 

[stapel]

Since the question says to solve, rather than to graph, then, yes, this is not a graphing problem.

Your class and/or textbook should have covered some techniques for solving quadratic equations. Completing the square would be one method, but factoring would surely be quicker, and even the Quadratic Formula would be simpler.

Eliz.

 

[jhawk555]

We covered quite some time ago and I'd forgotten. Back on track now.

Thank you!

 

[Denis]

x^2 - 16x = 0

Did you "get back on track" this way: x(x - 16) = 0 ?

 

[jhawk555]

No.

I did x^2-16x=0

(-16)*1/2=-8

(-8)^2=64

x^2-16x+64=0

(x-8)^2

Is this wrong?

x^2 - 16x = 0

Did you "get back on track" this way: x(x - 16) = 0 ?

 

[Denis]

C'mon, Hawk; how can you start with x^2 - 16x = 0
and end up with x^2 - 16x + 64 = 0 :shock:

You can't go borrow a number like that :wink:

x^2 - 16x = 0 ; factor:
x(x - 16) = 0
To get 0 from a multiplication, at least one of the terms has to be 0, right?
SO x = 0 or x - 16 = 0
x = 0 or x = 16 : kapish?

 

[jhawk555]

Yes, I do see how you did this. I thought this was a "complete the square problem" and that is how I can come up with an answer like what I got. I used (1/2 x b)^2. Kapish?

C'mon, Hawk; how can you start with x^2 - 16x = 0
and end up with x^2 - 16x + 64 = 0 :shock:

You can't go borrow a number like that :wink:

x^2 - 16x = 0 ; factor:
x(x - 16) = 0
To get 0 from a multiplication, at least one of the terms has to be 0, right?
SO x = 0 or x - 16 = 0
x = 0 or x = 16 : kapish?

 

[Mrspi]

You could certainly do this by completing the square.

BUT.....if you add something to one side (like 64), don't you have to add it to the other side as well? (this is a very basic algebra concept):

x^2 - 16x + 64 = 0 + 64

(x - 8)^2 = 64

Now, take the square root of both sides.

But, as others have said, why don't you "keep it simple"?

x(x - 16) = 0

x = 0 or x - 16 = 0

Solve each of those.

You should get exactly the same answers by completing the square.

 

[jhawk555]

I definately like the other way better and it was simple. Thank you!

You could certainly do this by completing the square.

BUT.....if you add something to one side (like 64), don't you have to add it to the other side as well? (this is a very basic algebra concept):

x^2 - 16x + 64 = 0 + 64

(x - 8)^2 = 64

Now, take the square root of both sides.

But, as others have said, why don't you "keep it simple"?

x(x - 16) = 0

x = 0 or x - 16 = 0

Solve each of those.

You should get exactly the same answers by completing the square.