Question

Solve each quadratic, leave answers as simplified radicals as necessary. 3x^2-13x=10

Answer 1

Quadratic is ax^2+bx+c=0 So what do you do first?

Answer 2

Well, set it equal to zero. So \[3x ^{2}-13x-10=0\]

Answer 3

Yep..now solve using the quadratic formula.

Answer 4

Alright, here is what I got: x=-2/3 and x=5

Answer 5

Did you plug them into the equation to verify they work?

Answer 6

I am right now, one moment.

Answer 7

They both equal zero.

Answer 8

But something tells me that I must try it with ten out of the modified equation.

Answer 9

If they both equal 0 then they are right.

Answer 10

Alright, that is one down, may I show you the next one?

Answer 11

OK

Answer 12

Alright, for these I have a feeling my current answers are incorrect. \[2x ^{2}-8x=6\]

Answer 13

Same thing we did above

Answer 14

Here are my answers: \[x=-\sqrt{7}-2 \]

Answer 15

I got a positive version of the above as well.

Answer 16

How would I check my answer?

Answer 17

Let's do this the easy way. First move the 6 and what does the equation look like?

Answer 18

\[2x ^{2}-8x-6=0\]

Answer 19

Now simplify that equation to get what?

Answer 20

\[2(x^{2}-4x-3)\]

Answer 21

I do have a feeling that I should've used the quadratic, but my gut led me with this.

Answer 22

Actually just x^2-4x-3=0

Answer 23

Where does the 2 go?

Answer 24

We are simplifying not factoring. We just divided everything by 2.

Answer 25

Alright. So, do I apply the quadratic still?

Answer 26

yes

Answer 27

But stop because you have the right answer above.

Answer 28

\[2+/- \sqrt{7}\]

Answer 29

Alright.

Answer 30

Now this one I couldn't figure out how to do to save my life.

Answer 31

2x^2+3x+4=0

Answer 32

Plug into the formula

Answer 33

\[-3\pm \sqrt{3^{2}-4(2)(3)}\div4\]

Answer 34

That it?

Answer 35

4(2)(4) I believe so what does that give you?

Answer 36

So, 9-32.