Write 2x^2 + 6x + 6 in the form a(x^2 + b) + c by completing the square.
2x2 + 6x + 62(x2 + 3x + 3) => Factor out 4 from each term so the x2 term of the quadratic has 1 for a coefficient.2[(x + 3/2)2 - d + 3] => Here, we've divided 3x by 2; this coefficient becomes b. When you expand the internal bracket however, you will be left with an additional term. This term is d. We don't want this term, so we subtract this from the quadratic.(x + 3/2)2 = (x + 3/2)(x + 3/2) => Don't make the mistake of just squaring each individual term!= x2 + 3x + 9/4 => 9/4 = d2[(x + 3/2)2 + 3/4] => 3 - 9/4 = 3/4Therefore the final answer is...2(x + 3/2)2 + 3/2(Expand the final term back out so you know you have the right answer.)
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