Question 134016
i dont know if you have worked with imaginary numbers or not so if this isnt what your looking for than im sorry
but to solve the equation (3x-2)^2=-9 the first thing you need to do is put the square root over the numbers so it would be

square root of(3x-2)^2= square root of -9
the square root of (3x-2)^2 cancels out because there is a square root and a power of 2. the equation should now look like this

3x-2=square root of -9
this is where the imaginary number comes in
since you cant take the square root of a negative number you have to replace the number with an i.
so the square root of -9 would now be 3i.
now the equation looks like this.
3x-2=3i
now to get the x by itself you now need to add 2 to both sides.
3x-2+2=3i+2
3x=3i+2
now we need to make the 3 go to the other side and since it is connected to the x we need to divide instead of add or subtract.
3x/3=(3i+2)/3
the three cancels
x=(3i+2)/3
im not totally positive if the 3 cancels out on the (3i+2)/3 part because its on an imaginary number but i think it does. im not going to do it because its not wrong the way i have it, but it might be able to be reduced. so ask your teacher if you want to. im sorry though.