Question

Please Helppp !!!!
Solve 5x2 = -30x - 65.

x = -3 ± 2i

x = -3 ± 4i

x = -6 ± 2i

x = -6 ± 4i

Answer 1

Do you know the Quadratic formulae?

Answer 2

yes, i do know the quadratic formula

Answer 3

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

Answer 4

Rearrage your eqn in quadratic form \[ax^2 + bx + c = 0\]subst a, b, c and solve for x

Answer 5

hold on , let me try

Answer 6

i'm kind of confused

Answer 7

Which part?

Answer 8

Putting all together : \[\text{Putting all together: } x = \frac{ -30\pm \sqrt{30^2 - 4*5*65}}{ 2*5}\]

Answer 9

\[ax ^{2}+bx+c+0 \]
When i substitute them i get \[5x ^{2}+30x-+65=0\] ?

Answer 10

When you move the expression on the right to the left, the -ve signs turn +ve. You remember?

Answer 11

yes,

Answer 12

\[\text{So you get : } 5x ^{2}+30x +65=0\]

Answer 13

i also remember that when solving the quadratic formula there was something that i have to do first, and i can't remember if it's the bottom half of the equation that i start with, or the part that says 30^2 - 4*5*65

Answer 14

\[\text{Simplify this further: } x = \frac{ -30\pm \sqrt{30^2 - 4*5*65}}{ 2*5} \rightarrow x = \frac{ -30\pm \sqrt{900 - 1300}}{10}\]

Answer 15

Does that make sense now?

Answer 16

\[x = \frac{ -30\pm \sqrt{900 - 1300}}{10} = \frac{ -30 }{ 10 } \pm \frac{ \sqrt{-400} }{ 10 }\]

Answer 17

and next you do 900 - 1300 and get \[x= -30\pm \sqrt{-400} / 10\]

Answer 18

or do i make the 400 positive ?

Answer 19

Nope, that's where the imaginary number 'i' comes in, since we do not the negative square root of a number...

Answer 20

ok

Answer 21

You have it rather like this\[x = -3 \pm \frac{ \sqrt{400i} }{ 10 } \rightarrow x = -3 \pm \frac{ 20i }{ 10 } \]

Answer 22

\[x = -3 \pm 2i\]

Answer 23

wow that is confusing, haha

Answer 24

It's very important you understand every bit of the process that got us here. So, what confusion can we clear up now?

Answer 25

the imaginary number is whats confusing me

Answer 26

Yeah, it's just a rule. You know that now, it won't confuse you any more :)

Answer 27

ohh i see, the 0's cancel out

Answer 28

Yeah

Answer 29

And you notice that we took the sqrt of 400 too

Answer 30

wait, what happened with the sort of 400 ? it canceled out too ?

Answer 31

You just keep the i out of it and take the square root of its coefficient.