Solve. 2x2 + 20x = –38

a. –5 ± √14
b. –5 ± √51
c. –5 ± √6
d. –5 ± √13

Question

Solve. 2x2 + 20x = –38

a. –5 ± √14
  b.  –5 ± √51
  c.  –5 ± √6
  d.  –5 ± √13

anonymous · Answer

c as usual.  why is it always c?

anonymous · Answer

can u show me how, though, im trying hard to remember but its not coming to me...

anonymous · Answer

ok first off each term has a factor of 2, so we can make our life easier by writing 
$$x^2+10x=-19$$

anonymous · Answer

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 · Answer

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 · Answer

oh i get it now, and this is for all problems like this?

anonymous · Answer

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 · Answer

oh okay, thanks. can u also help me with http://openstudy.com/study?F295750376716BE3I5S=_#/updates/4f178119e4b0aeb795f57dc2

anonymous · Answer

if the coefficient of the "middle term" is even, then it is much easier to complete the square