Question

What are the solutions of 3x2 + 15 = -6x?

-1 ± i

-1 ± 2i

-2 ± i

-2 ± 2i

Answer 1

okay let's solve it

let's 3x^2+6x+15=0

let take three as common factor

we get

3(x^2+2x+5)=0

now as \[3\neq0\] we have x^2+2x+5=0

by comparing it with standard form ax^2+bx+c

we get a=1 b=2 c=5

but this values in

\[x=-b \pm \sqrt{b ^{2}-4ac}/2a\]

Answer 2

Would it look like this?

Answer 3

correct ..! genius..! now let's further simplify it..

we can write by simplification as

\[x=-2 \pm (\sqrt{16} \sqrt{-1})/2\]

as you know \[\sqrt{-1}=i\] and \[\sqrt{16}=4\]

so we can write
\[x=-2\pm 4i/2\]

which is equal to \[x=-1\pm2i\]

i hope you got it.!! :)

Answer 4

Thanks. :)

Can you help me with one more?

Answer 5

yes i would love to..! let's solve it

Answer 6

What are the solutions of 4x2 + x = -3?

the quantity negative 1 plus or minus 7i all over 8

the quantity negative 1 plus or minus i square root of 5 all over 2

the quantity negative 1 plus or minus i square root of 47 all over 8

the quantity negative 1 plus or minus 2i square root of 7 all over 8

Answer 7

I've gotten this so far:

Answer 8

4x^2 + x = -3
4x^2 + x + 3 = 0
a=4, b=1, c=3
Substitute a, b and c in the quadratic formula.

Answer 9

\[x = \frac{ -1 \pm \sqrt{(-1)^{2} - 4(4)(3)} }{ 2(4) }\]

Answer 10

\[x = \frac{ -1 \pm \sqrt{1 - 48} }{ 8 } = \frac{ -1 \pm i \sqrt{47} }{ 8 }\]

Which answer matches the above?