Question

complete the square.
-4x^2-16x+3=0

Answer 1

i know that the answer is -4(x+2)^2+19 but i don't know how to get there..

Answer 2

oops rewrite it as

\[-4x^2 -16x = -3\]

is that ok..?

Answer 3

yes and i know the next step would be
\[-4(x ^{2}+4x)=-3\]

Answer 4

great... so what is needed inside the brackets to complete the square..?

Answer 5

\[-4(x ^{2}+4x+4)=-3+4\]

Answer 6

\[-4(x+2)^{2}=1\]

Answer 7

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

Answer 8

.. i don't get that part

Answer 9

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...?

Answer 10

OH.. 16.. because of the 4 that i factored out before.. so now i have to factor it back in

Answer 11

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

\[-4(x + 2)^2 + 19 = 0\]

Answer 12

It feels great to finally understand how to complete the square after 3 years. thanks

Answer 13

lol.. well it is tough when the coefficient of x^2 isn't 1

Answer 14

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