Question

solve using the quadratic formula. 9x^2-15x+25=0

Answer 1

I'm stuck on \[15 +- \sqrt{-15^{2}-900}/18\]

Answer 2

\[ax^2+bx+c=0\]\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
\[9x^2-15x+25=0\]\[x=\frac{15\pm\sqrt{(-15)^2-900}}{18}\]

Answer 3

I have that down I just don't know how to simplify it.

Answer 4

\[(-15)^2=(-15)\times(-15)=\]

Answer 5

225?

Answer 6

\[(-)(-)(15)(15)=(+)(5+10)(5+10)=(5\times5+2\times5\times10+10\times10)=255\]

Answer 7

yeah

Answer 8

so now what is 225-900?

Answer 9

-675

Answer 10

do i have to do\[\sqrt{-675} \]

Answer 11

?

Answer 12

[ sorry, i got disconnected]

Answer 13

That's right so far

Answer 14

When you have a parabola that is of this form\[y=ax^2+bx+c\]
and and the discriminant \(\Delta=b^2−4ac\)

There are three cases
\(\Delta<0\) will not touch x axis - there will be no real solutions
\(\Delta=0\) will touch x axis at one place only - one solution
\(\Delta>0\) will touch x axis exactly twice - two solutions

Answer 15

the quadratic formula
\[x=\frac{-b\pm\sqrt{\Delta}}{2a}\]

Answer 16

In your case the discriminant is negative, and the formula would have us take the square root of a negative number
no real number is the square root of a negative. so there are no real solutions for x
- [ this would give complex solutions but im not sure if you are looking for them ]

Answer 17

Are the complex solutions the same thing as imaginary solutions? I need imaginary solutions.

Answer 18

Yes, they are the same thing.

Answer 19

Do you know how I would get them for this problem?

Answer 20

do you have \(\frac{ 15\pm \sqrt{-675} }{ 18 }\)? then you would want to simplify.

Answer 21

Yes, that's exactly what I have right now. I'm not sure where to go from here.

Answer 22

okay, I assume you're having trouble with simplifying \(\sqrt{-675}\) ?
If so, first you want to break it up. I can rewrite it as \[\sqrt{-1}\sqrt{675} = \sqrt{-1}\sqrt{25}\sqrt{27}=\sqrt{-1}\sqrt{25}\sqrt{9}\sqrt{3}\]

Answer 23

\[\sqrt{25}=5 \]
\[\sqrt{9}=3\]
\[\sqrt{-1} = i \]
right?

Answer 24

Yes but don't forget you'll have the remaining \(\sqrt{3}\)

Answer 25

How would I write that? Do I just multiply 5 and 3 and write \[\sqrt{3}i\] next to it?

Answer 26

Yes, although I usually see i before the square root.

Answer 27

So now I have\[x=15 \pm 15i \sqrt{3} / 18\]

Answer 28

Yes

Answer 29

That's not the answer, is it? Isn't there more to do?

Answer 30

Is the answer different from the given answer? You can separate the +/- I guess

Answer 31

No, it's not multiple choice. I just thought there was more to it. Thank you.

Answer 32

cancel the common factor of three

Answer 33

NB: the solutions are complex solutions.
A number is complex when it has an imaginary And a real part,