## anonymous one year ago complete the square. -4x^2-16x+3=0

1. anonymous

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

2. campbell_st

oops rewrite it as $-4x^2 -16x = -3$ is that ok..?

3. anonymous

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

4. campbell_st

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

5. anonymous

$-4(x ^{2}+4x+4)=-3+4$

6. anonymous

$-4(x+2)^{2}=1$

7. 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

8. anonymous

.. i don't get that part

9. 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...?

10. anonymous

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

11. 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 $-4(x + 2)^2 + 19 = 0$

12. anonymous

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

13. campbell_st

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

14. 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