I have a test tomorrow and I was given the study sheet today. These are summer classes, so things are a bit rushed.

My questions involve solving for real and or imaginary solutions to a quadratic equation using quadratic formula and one involving completing the square to solve an equation.

Problem one states "Find all real solutions."

(3x -4)^5/2 = 32

I start off by distributing to get:

15/2x - 20/2 = 32

I then multiply by two on both sides to receive:

15x - 10 = 64

From here, I am puzzled. I am not sure if I am supposed to complete the square or solve for x or use quadratic formula or what.

If I solve for x, I end up with 74/15.

Problem two states "Find all real and/or imaginary solutions."

3x^2 - 4x + 5 = 0

I use quadratic formula on this problem to get:

4(plus/minus) the square root of (-4)^2 - 4(3)(5)

over

2(3)

So, I am left with:

4(plus/minus) the square root of -44 over 6

then

4(plus/minus) 6.63i over 6

So, my solutions are

10.63i/6 which equals 1.77i

and

-2.63i/6 which equals -0.44i

I am not sure as to whether or not I worked this one out properly.

My third and final problem states "Solve the equation by completing the square."

3x^2 - 12x -9 = 0

First off, I divide the problem by 3 to get:

x^2 - 4x - 3 = 0

Then I add three to both sides and square it off to get:

x^2 - 4x + 4 = 7

and I am left with:

(x - 2)^2 = 7

I square everything off and get:

x - 2 = the square root of 7

which then turns into:

x=2(plus/minus) the square root of seven.

I am confident that I worked this one out correctly, but I am unaware as to whether or not I will need to break this one down further or not to get a real solution set.

Any help is more than appreciated. Thank You. )