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i know that the answer is -4(x+2)^2+19 but i don't know how to get there..
oops rewrite it as
\[-4x^2 -16x = -3\]
is that ok..?
yes and i know the next step would be
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great... so what is needed inside the brackets to complete the square..?
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
.. i don't get that part
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...?
OH.. 16.. because of the 4 that i factored out before.. so now i have to factor it back in
so the value has to be -16
so you get
-4(x^2 + 4x + 4) = -3 -16
-4(x + 2)^2 = -19
\[-4(x + 2)^2 + 19 = 0\]
It feels great to finally understand how to complete the square after 3 years. thanks
lol.. well it is tough when the coefficient of x^2 isn't 1
This way might be easier:
-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
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