Complete the square.
1. x^2 + 12x + ______
2. x^2 - 6x + ______
Solve by completing the square.
3. x^2 - 6x = 16
4. 2x^2 - 3x + 1 = 0
5. x^2 - 4x - 5 = 0
i suppose for these two questions you just want us to add the constant that will make each a complete square. so i will do that.
in the expanded form of complete squares, the lone constant is always the square of half the coefficient of x.
1. x^2 + 12x + (12/2)^2 will give a complete square.
=> x^2 + 12x + 6^2
=> (x + 6)^2 is the completed square
2. x^2 - 6x + (-6/2)^2
=> x^2 - 6x + (-3)^2
=> (x - 3)^2 is the completed square.
now since we are in an equation, adding constants have consequences. now when we add something, we have to add it to the other side as well. before we add anything, we want to make sure that the coefficient of x^2 is one, so we are ok here.Solve by completing the square.
3. x^2 - 6x = 16
x^2 - 6x + (-3)^2 = 16 + (-3)^2
=> (x - 3)^2 = 16 + 9
=> (x - 3)^2 = 25
=> x - 3 = +/- sqrt(25)
=> x = 3 +/- sqrt(25) = 3 +/- 5
=> x = 8 or x = -2
why don't you try the rest to see if you get it. i didn't go into detail about completing the square, so i don't know if you're understanding the process
You are correct, good job!!!
your steps seem weird though. all the numbers are correct, but the way you did it, you can't really see the process...but who cares! if you know what your are doing, and you get the right answer and the method is reasonable, you're good!
there are more right? try the rest