Question

Find the exact solutions and simplify as much as possible for 5x^2+8=12x

Answer 1

5x^2 - 12x + 8 = 0
this will not factor so use quadratic formula

x = [-b +/- sqrt((b^2 - 4ac) ] / 2a

here a=5,b=-12 and c = 8

Answer 2

So, how does i come in to play?

Answer 3

So for instance, when I use the calculator I get 6/5+(2/5)i, 6/5-(2/5)i

Answer 4

x = [-(-12) + sqrt(144-4*5*8) ] / 10
= 12 + sqrt(-16)
------------
10

= 12/10 + (4/10) i
= 6/5 + (2/5)i

- other root is calculated in similar way

Answer 5

But what is the i?

Answer 6

i = sqrt(-1) - the roots are complex numbers

a + bi is complex number where a = real part and bi is imaginary part

there is no real square root of a negative number

Answer 7

ahhhhhh ok

Answer 8

Thank you very much!

Answer 9

yw