help please! how do you solve this quadratic equation by completing the square: -x^2+6x+10=0

Question

nottim · Answer

What adds to six and multiplies to 10.

nottim · Answer

Or is it the other way around?

hero · Answer

-x^2 + 6x + 10 = 0
-(x^2 - 6x - 10) = 0
x^2 - 6x - 10 = 0
x^2 - 6x = 10
x^2 - 6x + 9 = 10 + 9
(x - 3)^2 = 29
x - 3 = + or - sqrt(29)
x = + or - sqrt(29) + 3

anonymous · Answer

this isn't that kind of problem. you are suppose to make it be a perfect square. I got to this...
-x^2+6x+10=0
              -10
-x^2+6x=-10
Now you have to force it to become a perfect square.
soo... -x^2+6x+9=-10+9
sqrt -(x+3)^2= sqrt -1
-x+3= sqrt -1
-x=-3 + or - sqrt -1
then I am confused!

hero · Answer

^well, you were supposed to add 10 to both sides, then you would have gotten 10 + 9 = 29 instead of -1

hero · Answer

By the way, I did make it a perfect square. I know how to "complete the square" and that's what I did.

anonymous · Answer

nooo you have subtract -10 and then add nine because you had to subtract to cancel out the ten to make it zero on the left side so zero minus 10 is -10 and then you have to make the perfect square & you did. but you just messed up on the end part. I just don't understand how to simplify the ending. My teacher did not go over this well in class..

anonymous · Answer

But I was replying to @NotTim

anonymous · Answer

But thank you anyways,
:)

hero · Answer

Trust me @apeymarie93, I know what I'm talking about.

hero · Answer

@apeymarie93

hero · Answer

You failed to understand my first two steps

pokemon23 · Answer

LOL what a coincidence me and hero was doing this

hero · Answer

That would be the appropriate course of action that would ultimately lead to having to add 10 to both sides, rather than subtract it.

hero · Answer

Uh, no Pokie..this is complete the square

hero · Answer

@pokemon23

anonymous · Answer

Ohh I see! How would do this one then?
x^2+2x-7
I got.
x= -1 + or - 2 sqrt 2

pokemon23 · Answer

@Hero THEIR MORE

hero · Answer

x^2 + 2x - 7 = 0
x^2 + 2x = 7

this is the same thing that I was explaining with pokie earlier....the leading term must be positive before proceeding...In this case, x^2 is positive, so yes, we can simply add 7 to both sides. 

if it were: 

-x^2 + 2x - 7 = 0

we would have to do this: 
-(x^2 -2x + 7) = 0
x^2 - 2x + 7 = 0
x^2 - 2x = -7

Do you get the difference now?

hero · Answer

I probably confused you. I should have just posted the solution first.

anonymous · Answer

I am completely confused...

hero · Answer

I know, and I apologize. I was just trying to help you understand the difference of approach when you have something like

x^2 + 6x + 7 = 0

vs

-x^2 + 6x + 7 = 0

hero · Answer

The first step is not the same with those two

anonymous · Answer

Oh so if you have -x^2 you have to factor out the negative?.....?

hero · Answer

precisely

anonymous · Answer

So like did i do the other one right? My teacher went over this in like 10 minutes Friday. I get like the all the steps now, but like.. I don't understand the very last step.

hero · Answer

which very last step? Why don't you post your full solution to this and then put an arrow next to the step you don't get?

anonymous · Answer

Like where you have to simplify  the square root. 
Hold on one second.

anonymous · Answer

x^2+2x -7=0
x^2 +2x + 1=8
sqrt(x+1)^2 = sqrt 8
x= -1 + or - sqrt(8)
How do you simplify it down?

hero · Answer

You don't

hero · Answer

That's the end of it

anonymous · Answer

But the answer in the back of my book says.
x= -1 + or - 2 sqrt (2)

hero · Answer

I was just about to mention that...sqrt(8) = sqrt(4*2) = 2 sqrt(2)

that's why I came back.

anonymous · Answer

See, that's what I don't understand..