Question

Quadratic equations... A nightmare for me since I'm not gifted in math. To top it off, my homework is asking two questions about this equation. The first question is to pick the appropriate form. The two forms I can pick are (x+?)^2=? or (x-?)^2=? I also have the pleasure of needing to fill in the ?. The equation needing solved for is: x^2+6x-5=0
I do not understand how to solve this... any help, and I mean any, would be really appreciated!
Yours truly,
A brain fried kid

Answer 1

The equation can be solved using the quadratic equation
x= [-b +-(sqrt(b² -4•a•c)] / 2•a
In the equation you posted a=1 b=6 c=-5
So,
x = [-6 +-(sqrt(36 -4•1•-5)] / 2•1
x = [-6 +-(sqrt(56))] / 2
x = -6 +- (7.4833147735) / 2

x1 = 1.4833147735 / 2
x1 = .74166

x2 = -13.4833147735 / 2
x2 = -6.7417

Answer 2

Thank you! So what does the appropriate form part mean in my original question? I'm not sure why they are asking that

Answer 3

I just joined this site 10 mins ago, so I'm not sure how to write a good review or rating of someone, but I am planing on writing one for you once I understand all this!

Answer 4

So the 2 solutions are .74166 and -6.7417

The factors that created this quadratic equation are:
(x -.74166) • (x +6.7417)

If you are unfamiliar with quadratic equations then the last 2 postings I made are probably meaningless to you am I right?

Answer 5

You sure have a lot of patience... I hope I can test it a tiny bit more. I still don't understand how this fits in to the (x-?)^2=? or (x+?)^2=? part. I love english, thank goodness some people like you enjoy math!!

Answer 6

Hi Laylaj - I wouldn't worry about crediting someone (but you could click the "best response" button next to my name).
Thanks
Still you'll need to learn something about quadratic equations right?

Answer 7

Thanks Laylaj - I'm willing to stick around some more if you wish.

For one thing, when they are asking that (X+ ?)^2 = ? question is that EXACTLY how it is worded?
Could you copy and paste the question to make sure we know PRECISELY they are asking.

Answer 8

Sure thing! I'll be back in a minute

Answer 9

Okay

Answer 10

It says: solve the equation by completing the square x^2+6x-5=0
First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. List all solutions if multiple are found.
Then there are two options with blanks for me to pick the "appropriate form" a) (x+?)^2=? or b) (x-?)^2=? and then c) my answer(s) to what x is for the quadratic equation.

Answer 11

They want that solved by completing the square - I can do that but I think that would be more difficult for you to understand than the quadratic formula.

So completing the square:
x^2+6x-5=0

To complete the square:
x^2+6x-5=0
Move the "non X" term to the right:
x²+6x=+5

Divide the equation by the coefficient of X² which in this case is 1 so there's no change
x²+6x=+5

Now for "completing the square" we:
take the coefficient of X which is 6
divide that by 2 making it
3
square that number
9
then add it to both sides of the equation
x²+6x +9 =+5+9

x²+6x +9 =+14

Take the square root of BOTH sides of the equation
(x+3) = sqrt(14)

The sqrt(14) = 3.7416573868 AND it is -3.7416573868

x = 3.7416573868 -3
x= .7416573868

x = -3.7416573868 -3
x = -6.7416573868 -3

There are the answers from completing the square.

Answer 12

Actually that last line should just be x = -6.7416573868
WITHOUT the -3 at the end

Answer 13

Oh gosh.. I'm not feeling very bright at the moment. I do understand how the completing the square makes sense. (a little bit, at least the formula part but not why it works)
But how does that fit in to the (x-?)^2=? or (x+?)^2=? ? I only need to answer and fill in one of these options.

Answer 14

That "squaring" part bothers me too.
If the equation were a perfect square:
example x² + 6x +9 = 0 IS a perfect square and you could say it equals
(x +3) ^2
However, x^2+6x-5=0
is NOT a perfect square and it CANNOT be placed into a compact form such as (x+?)^2

Answer 15

To solve a quadratic equation you can always use
1) quadratic formula
2) factoring
3) completing the square
You always have those 3 choices and I find it strange that they always teach you to learn all three when you need just one.
I always prefer the quartic formula - always.

Answer 16

made a typing mistake again - the last line should be quadratic formula and not quartic

Answer 17

That really makes me wonder why they are asking me that then. Hm. Well, thank you SO much for your very informative and kind answers. I'm glad that part of the question doesn't make sense to someone else besides me. As I am moving into that part of my math book I am now a loyal supporter of the quadratic formula. Thank you, wolf1728.
Happy math solving!
Layla

Answer 18

Thank you very much LaylaJ

Answer 19

and thanks for the medal :-)

Answer 20

:D