Hey guys,
I'm doing work on completing the square.
There is one small thing I don't understand with the kind of question I have attached. (solve for x)
When you don't get an (x+b)^2=0 expression but instead get an (x+b)^2=a expression,
the textbook will give the solution to x as x = -b+(root)a
I guess they want to just do x+b inside the brackets, be left over with (root)a and then square (root)a to have a=a.
Is this legal? When expanding a binomial multiplied by a binomial, don't you have to cross multiply?
Won't this equation be left with a 2bx to imbalance the equation?
Many thanks,
Corey
I'm gonna be honest - I have no clue what you're asking. What I do know is, looking at your attachment, that's wrong.
Everything is fine up until line 4. When moving from line 3 to line 4, you've removed the square from the brackets. Where has it gone? Remember - things can't just disappear in maths, they have to move somewhere or you must change both sides of the equation. On top of that, when you moved that 17/4 to the other side, you forgot to change its sign to +17/4. To remove the square from the brackets (and this is what the book is doing), you should take the square root of both sides. This will cancel out the squaring of the (x+5/2)^2, and leave a square root on the other side. However, since you don't know if +sqrt(17)/2 or -sqrt(17)/2 led to (x-5/2)^2, you will need to leave the second square root as +/-, just as the book does. The plus/minus thing might sound complicated, so I will come back to it. First, here's how the working should look, for full clarity:
On the plus/minus thing, imagine your equation is x^2=4. This is real simple, right - you square a number, it equals 4. What is that number? Well, there are two numbers that become 4 when you square them - 2^2=4, because 2*2=4. However, (-2)^2 ALSO equals 4, because a negative times a negative makes a positive. Hence, (-2)^2=-2*-2=4. So, the solution to x^2=4 ISN'T x=2, it's actually x=-2 OR 2. We commonly write this as x=-2,2, or as x=plus/minus 2.
Some of that you may have already known, but again, had no clue what you were actually asking, so had to make some guesses. Let me know if I haven't solved your confusion, and maybe try rewording what you're having trouble understanding?