SOLUTION: Solve by completing the square. z^2 + z = 2

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Question 1912: Solve by completing the square.
z^2 + z = 2

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
to write the lefthand side as a "square" eg %28z%2B3%29%5E2 we need to figure out what is missing and add it in, so the standard square is as follows:
%28x%2Ba%29%5E2+=+x%5E2+%2B+2ax+%2B+a%5E2
so, we would need to find the number "a"...so look at the coefficient of the x-term. You have 1z so 2a is equivalent to 1 therefore a itself must be 1/2. If that is so, then a%5E2 must be 1/4.
so, we would need to have z%5E2+%2B+z+%2B+%281%2F4%29
but we cannot JUST add a 1/4 to one side...we need to add it to both sides, to keep the equation "unchanged", so we actually get the following:
z%5E2+%2B+z+%2B+%281%2F4%29+=+2+%2B+%281%2F4%29
which becomes
%28z%2B%281%2F2%29%29%5E2+=+%289%2F4%29
so now, taking square root of both sides, we get
z%2B%281%2F2%29 = +-%283%2F2%29....ALWAYS remember the +- when square rooting!!!!
so z+1/2 = 3/2 or z+1/2 = -3/2
so z=1, or z=-2
Make sense?
cheers
Jon.