Question

Jimmy began deriving the quadratic formula as shown.

Answer 1

ahhh this is a fun question
but don't have time rn :(
ignore all the work on the pic just start from the 1st step
Ax^2+Bx+C=0
complete the square

Answer 2

Multiply \(\dfrac{b}{a}x\) by \(\dfrac{2}{2}\)

Answer 3

That should be the next step.

Answer 4

@Hero

Answer 5

I know the correct answer but I cannot tell you what it is outright.

Answer 6

@hero ok

Answer 7

@hero how can i find the answer?

Answer 8

One of the answer choices gives away the explanation.

Answer 9

But the truth is the actual next step (what I mentioned above) is not included in the answer choices.

Answer 10

One cannot proceed without conducting that particular step.

Answer 11

Subtract x² from each side?

Answer 12

They give you the following steps:

\(ax^2 + bx + c = 0\)

Divide both sides by a:
\(x^2 + \dfrac{bx}{a} + \dfrac{c}{a} = 0\)

Subtract \(\dfrac{c}{a}\) from both sides:
\(x^2 + \dfrac{bx}{a} = -\dfrac{c}{a}\)

Add \(\left(\dfrac{b}{2a}\right)^2\) to both sides:
\(x^2 + \dfrac{bx}{a} + \left(\dfrac{b}{2a}\right)^2 = -\dfrac{c}{a} + \left(\dfrac{b}{2a}\right)^2\)

Answer 13

At this point, you're supposed to know to multiply the middle term of the left hand side by \(\dfrac{2}{2}\) to get:
\(x^2 + \dfrac{2b}{2a}x + \left(\dfrac{b}{2a}\right)^2 = -\dfrac{c}{a} + \left(\dfrac{b}{2a}\right)^2\)

Answer 14

Thats not a choice though.

Answer 15

I'm not done yet

Answer 16

Then you would split the middle term to get:
\(x^2 + \dfrac{b}{2a}x + \dfrac{b}{2a}x +\left(\dfrac{b}{2a}\right)^2 = -\dfrac{c}{a} + \left(\dfrac{b}{2a}\right)^2\)

Then expand \(\left(\dfrac{b}{2a}\right)^2\) to get:
\(x^2 + \dfrac{b}{2a}x + \dfrac{b}{2a}x +\dfrac{b^2}{4a^2} = -\dfrac{c}{a} + \dfrac{b}{4a^2}\)

Answer 17

Then:
\(x\left(x + \dfrac{b}{2a}\right) + \dfrac{b}{2a}\left(x + \dfrac{b}{2a}\right) = -\dfrac{c}{a} + \dfrac{b}{4a^2}\)

Answer 18

And then you factor the common term on the left hand side of the equation to get:
\(\left(x + \dfrac{b}{2a}\right)\left(x + \dfrac{b}{2a}\right) = -\dfrac{c}{a} + \dfrac{b}{4a^2}\)

Which simplifies to
\(\left(x + \dfrac{b}{2a}\right)^2 = -\dfrac{c}{a} + \dfrac{b}{4a^2}\)

Answer 19

All of that is the process of factoring the trinomial.

Answer 20

There's a typo in the steps unfortunately.

Answer 21

The steps are correct otherwise

Answer 22

hey hero, if you tell me what the error is i'll fix it ._.

Answer 23

On the right hand side, the last term should be \(\dfrac{b^2}{4a^2}\) everywhere you see \(\dfrac{b}{4a^2}\)

Answer 24

@pandasurvive are you good now?

Answer 25

http://prntscr.com/f32ir5 so like this?

Answer 26

And panda is currently AFK

Answer 27

No, that doesn't look right.

Answer 28

Don't worry about it @Ultrilliam

Answer 29

ok then ._.

Answer 30

Just try to work on the edit button. It would greatly improve the quality of my responses.

Answer 31

@hero thank you

Answer 32

You're most welcome. Anytime