Question

[Fan + Medal] Find the real or imaginary solution of the equation below by factoring.


4x^2 = -4x -1.

Answer 1

\[4x ^{2}+4x=-1\]\[x(x+1)=-\frac{ 1 }{ 4 }\]

Answer 2

@caozeyuan Wouldn't that only be x^2 + x = -1/4?

Answer 3

I skiped a step, if you divide LHS and RHS of top eqn by 4, you get the eqn you just wrote

Answer 4

Ah. Makes sense now. Could you help on one more? I'm not the best at factoring ¯\_(ツ)_/¯

Answer 5

sure

Answer 6

Okay, it's: 2x^2 + 3 = 4x

Answer 7

Would I have to get the X's on one side and the 3 on the other side first?

Answer 8

let me see, give me one sec

Answer 9

divide by 2 to make the coeff of x^2 1 and then move all x's to LHS, and constants to RHS

Answer 10

since b^2-4ac is less than 0 we know it has complex roots so we can assume x = a+bi, pultiply through and let imarginary part be 0 and real part be your constant

Answer 11

So what would the final answer come out to be then? This is confusing.

Answer 12

did you get the eqantion to be x(x-2)=-3/2

Answer 13

Okay so it would be

2x^2 + 3 = 4x
2x^2 - 4x = -3.
/2
x^2 - 2x = -3/2
x(x -2) = -3/2?

Answer 14

yes, great

Answer 15

do you know why it has no real roots?

Answer 16

No, not really?

Answer 17

a quadratic equation takes the form ax^2+bx+c=0 where a is not zero, correct?

Answer 18

the determinant of this equation is b^2-4ac, and if it is negative we have complex roots only, and the roots are conjugate pair i.e. one is a+bi and the other is a-bi where i^2=-1

Answer 19

Okay, that makes a lot of sense now. Thank you :)

Answer 20

now, for this equation the determinant is negative so we dont have real roots

Answer 21

therefore we can assume x=a+bi

Answer 22

Are you good with polynomial long division? I need to check this answer I got.

Answer 23

Not really, but I can try, do you still want me to solve the equation?

Answer 24

No, that's fine. I should be able to get it from there.

And I'm supposed to divide (x^3 + 7x^2 + 15x + 9) by (x+1)
and the answer I got is x^2+6x+9.

Answer 25

let me try

Answer 26

yep, thats correct

Answer 27

Alright, great! Thank you for helping me :)