Question

Will reward with Medal!

What equation results from completing the square and then factoring?
x^2 - 10x = 46

please help.

Answer 1

My choices are here ... I'm confused

Answer 2

have you "completed the square" before? If so, what is the first step?

Answer 3

Not sure, could you go through some of the steps?

Answer 4

Look at x^2 - 10x = 46.
Re-write it as 1x^2 - 10 x =46 and compare this result to:
ax^2 + bx + c.

a=?
b=?

Answer 5

?

Answer 6

x^2 - 10x = 46

To complete the square, start with an equation that has x^2, not 2x^2 or 3x^2, etc.
In this case, you already have that.
Then move the constant term (term with no variable) to the right side. In this case this is already done since you have 46 on the right side.

Answer 7

Oh so it was already on the right side

Answer 8

The "complete the square" step is next.
Take the coefficient of the x term. Take half of it. Then square that. Then add that to both sides.

Answer 9

apex?

Answer 10

Johnny: those a, b and c are called coefficients. Specifically, they are the coefficients of the x-squared and x term of your polynomial expression. I asked you to do a comparison, a few lines earlier. a=1 and b =-10.

Be sure to spend enough time on this so that you understand and remember it and can identify those coefficients.

Again, b=-10. Take half of that, please (divide -10 by 2).

What's the result?

Answer 11

-5

Answer 12

x^2 - 10x + _____ = 46 + _____

The coefficient of the x term is -10.
Half of -10 is -5.
-5 squared is 25.
Add 25 to both sides and place the 25 as shown below (in the blanks above)

x^2 - 10x + 25 = 46 + 25

Answer 13

Good. Johnny: now square that result. In other words, square (-5). (-5)^2=??

Answer 14

Now factor the left side. It is the square of a binomial.
Also, add 46 and 25 on the right side.
That'll give you your answer.

Answer 15

It's 71
So my answer would be D

Answer 16

Right. In summary, Johnny: (-5)^2=25.
As mathstudent55 has already done, add 25 to both sides of your equation.

You'll get \[x^2 - 10x + 25 = 46 + 25\]

Answer 17

I believe

Answer 18

Both were helpful, thank you.

Answer 19

Please let's go through this problem solution step-by-step (even though I imagine you're anxious to get the "answer."

Actually, (-5)^2=25.

It's important that you recognize that you now have a perfect square trinomial on the left side. (On the right side you have the sum 69, which is also a perfect square.

I'm going to ask you to factor x^2 - 10x +25. This is a crucial skill in algebra. What are the factors?

Answer 20

@Johnny621 : I'm hoping you'll stick with this until we find the final solution. Sorry to say, it's not 71.

Answer 21

It worked out

Answer 22

So how could it not be?

Answer 23

Maybe just different ways of going about it ...

Answer 24

Would you mind demonstrating just what you did?
I've asked you to factor x^2 - 10 x + 25; would you mind doing that here and now?

Answer 25

As the other user said above, I took half of -10 then squared it. After that I took the answer and added it to the right side

Answer 26

46+25 = 71

Answer 27

Here's what I was looking for:

x^2 - 10x + 25 = 71
Factoring the left side produces

(x-5)^2 = 71.

Answer 28

How many answers would there be ? How many x values?

Answer 29

So you claim that it wasn't 71 but now it is?

Answer 30

Confusing my sleek-feathered one.

Answer 31

If (x-5)^2 = 71, what happens when you take the square root of both sides?

Johnny, if you don't care to spend the additional time to understand this question thoroughly, you don't have to. Please make up your mind. The answer is NOT 71. Rather, the expression that leads to solutions is (x-5)^2 = 71.

Answer 32

I wasn't saying that the answer entirely was "71" I was solving the next step that I was told to do. After I had done that step I had figured out the answer was "D".

Answer 33

Is there always a stick in your bum?

Answer 34

I understand you're only trying to help and I think that's great, don't get me wrong.

Answer 35

It's hard to tell what your intention is ...

Answer 36

You can help someone else if you're still around. I'll probably be back with another question soon though.

Answer 37

Lost my connection to the 'Net; sorry.
I'd suggest you be careful with your language: No matter how young or how old I am or how young or how old you are, "stick in your bum" is highly inappropriate here.

Answer 38

There are a lot of other phrases I had in mind ... anyway I'll try to think of something more "appropriate" next time.

Answer 39

I've noticed that you still have not answered several key, mathematical questions that I've asked you. I'm a retired math professor and I have a special fondness for asking students to demonstrate their knowledge instead of just pouring out answers. Unfortunately, if you can't or won't answer, it tells me you may not very well understand what we're doing. So I ask that you please try to answer my questions next time.

Answer 40

I'd suggest you just move on; work some other math problems. The more practice you get, the better.

Answer 41

Math isn't my best subject as you may have noticed. I had already got my answer. I knew the answer wasn't "71" and I apologize that you may have thought that was the case. I really don't understand much and I don't want to spend much time trying to. That's my choice as you said earlier. Congratulations on earning the title of retired math professor. I'll be back with another question for sure, try to have a nice day until then!