College Algebra problems.
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)
So, I am left with:
4(plus/minus) the square root of -44 over 6
4(plus/minus) 6.63i over 6
So, my solutions are
10.63i/6 which equals 1.77i
-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. :))