Question

solve x^2 +12x + 5 = 0

Answer 1

x = {12.403124237, -0.403124237}

Answer 2

You want to use the method of completing the square, are you familiar with that @thefourdcarrs ?

Answer 3

Yes except that there are no multiples of 5 that add up to 12 so would I have to use the quadratic equation formula?

Answer 4

Yes, the quadratic formula, or it's accomplice, the completing the square method.

Answer 5

Using this method, you are going to "form a quadratic function" inside the parenthesis.

Answer 6

Not sure how to do it by using completing the square method

Answer 7

You shall learn it today! :)

Answer 8

I appreciate your help

Answer 9

So first, group your x terms together like so: \((x^2+12x) +5=0\)

Answer 10

comparing the stuff inside the parenthesis to the quadratic formula, \(ax^2 +bx+c\), we see that we have part of it completed, the \(ax^2 +bx\) part.

Do you see that?

Answer 11

Yes

Answer 12

Alright :)

Now we want to compete the quadratic, so we need to find a \(c\) value that will satisfy the equation.

We can find that by taking our \(b\) value, dividing it by 2, and then squaring the whole fraction as so: \(c= \left(\frac{b}{2}\right)^2\)

Answer 13

Could you find the new c value for me?

Answer 14

not sure where to go from that part though factoring out the x (x+12) +5 = 0?

Answer 15

Not quite. Remember, we have part of our quadratic completed. therefore our \(b\) is 12 in this case.\[c=\left(\frac{12}{2}\right)^2 = 6^2=36\]

Answer 16

Then we input this back in to our equation. \[(x^2+12x+36) =-5+36\]What we add to one side of our equation, we must subtract to keep our reformatted equation consistent with our original equation.

I isolated our new found quadratic on the left side by subtracting -5 to both sides, and then added in the \(c\) value of our quadratic to both sides to stay consistent.

Answer 17

If it's not dimple and doesn't yield an imaginary answer, I prefer just using the quadrac formula. Factoring(ie completing the square, which I hate) is my personal last resort.

Answer 18

Oh, I love it!! Haha.

Answer 19

Quadratics are my last resort, haha.

Answer 20

simple* lol

Answer 21

It's too much effort to do completing the square haha

Answer 22

I've been rigorously practicing this method since coming to openstudy, and now I find it wonderfully simple :P

Answer 23

lol I just don't like it. I prefer a neat result.

Answer 24

that isn't neat to me