anonymous
  • anonymous
Solve. 2x2 + 20x = –38 a. –5 ± √14 b. –5 ± √51 c. –5 ± √6 d. –5 ± √13
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
c as usual. why is it always c?
anonymous
  • anonymous
can u show me how, though, im trying hard to remember but its not coming to me...
anonymous
  • anonymous
ok first off each term has a factor of 2, so we can make our life easier by writing \[x^2+10x=-19\]

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anonymous
  • anonymous
then we can write the left hand side as a perfect square , by taking half of 10, which is 5, squaring and adding it to both sides to get \[(x+5)^2=-19+25=6\]
anonymous
  • anonymous
then take the square root, don't forget the plus and minus \[x+5=\pm\sqrt{6}\] then subtract 5 \[x=-5\pm\sqrt{6}\]
anonymous
  • anonymous
oh i get it now, and this is for all problems like this?
anonymous
  • anonymous
yes you can always use this method. if you like you could write \[x^2+10x+19=0\] and then use the quadratic formula, but that would be more work because you would have a denominator, and then you would have to simplify the radical, factor and cancel to get the answer you see above
anonymous
  • anonymous
anonymous
  • anonymous
if the coefficient of the "middle term" is even, then it is much easier to complete the square

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