anonymous
  • anonymous
complete the square. -4x^2-16x+3=0
Mathematics
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anonymous
  • anonymous
complete the square. -4x^2-16x+3=0
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
i know that the answer is -4(x+2)^2+19 but i don't know how to get there..
campbell_st
  • campbell_st
oops rewrite it as \[-4x^2 -16x = -3\] is that ok..?
anonymous
  • anonymous
yes and i know the next step would be \[-4(x ^{2}+4x)=-3\]

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campbell_st
  • campbell_st
great... so what is needed inside the brackets to complete the square..?
anonymous
  • anonymous
\[-4(x ^{2}+4x+4)=-3+4\]
anonymous
  • anonymous
\[-4(x+2)^{2}=1\]
campbell_st
  • campbell_st
no you don't add 4.... you need to have \[-4(x^2 + 4x + 4) = -3 + (-4 \times 4)\] because of the common factor... think about what happens when you distribute
anonymous
  • anonymous
.. i don't get that part
campbell_st
  • campbell_st
ok... 4 inside the brackets is correct... \[-4(x^3 + 6x + 4) = -3\] so I'll distribute \[-4x^2 -16x - 16 = -3 +??\] after distributing what value on the left needs to be added to the right...?
anonymous
  • anonymous
OH.. 16.. because of the 4 that i factored out before.. so now i have to factor it back in
campbell_st
  • campbell_st
so the value has to be -16 so you get -4(x^2 + 4x + 4) = -3 -16 or -4(x + 2)^2 = -19 which becomes \[-4(x + 2)^2 + 19 = 0\]
anonymous
  • anonymous
It feels great to finally understand how to complete the square after 3 years. thanks
campbell_st
  • campbell_st
lol.. well it is tough when the coefficient of x^2 isn't 1
wolf1728
  • wolf1728
This way might be easier: http://www.1728.org/quadr2.htm -4x^2 -16x +3=0 1) Move the "non X" term to the right: -4x^2 -16x= -3 2) Divide the equation by the coefficient of X² which in this case is -4 x^2 +4x = .75 3) Now here's the "completing the square" stage in which we: • take the coefficient of X which is +4 • divide it by 2 which equals 2 • square that number which equals 4 • then add it to both sides of the equation. x^2 +4x +4 = 4.75 (X+2) * (x+2) = 4.75 4) Take the square root of both sides of the equation: x +2 = square root (4.75) x +2 = 2.1794494718 AND x +2 = -2.1794494718 x = .1794494718 x = -4.1794494718

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