Solve by completing the square: -2x^2-3x-3=0?

-2x^2 - 3x - 3 = 0
-2x^2 - 3x = 3 <== Added 3 to both sides
x^2 + 1.5x = -1.5 <== Divided both sides by -2

Note that completing the square requires a x^2 coefficient of 1. Once you do that, divide the middle term by 2, square that, and add that to both sides. This results in the left side being a perfect square.

x^2 + 1.5x + (1.5/2)^2 = -1.5 + (1.5/2)^2 <== Added (1.5/2)^2 to both sides
x^2 + 1.5x + 0.5625 = -1.5 + 0.5625 <== Simplify
x^2 + 1.5x + 0.5625 = -0.9375 <== Further Simplifying
(x + 0.75)^2 = √-0.9375 <== Convert the left side into a perfect square and square rooted both sides. Notice that we are in complex number territory now.
x + 0.75 = +/- ~0.968i

Splits into 2 solutions:
x + 0.75 = 0.968i
x = -0.75 + 0.968i

AND

x + 0.75 = -0.968i
x = -0.75 - 0.968i

So the solutions are {-0.75 + 0.968i, -0.75 - 0.968i}

There are no real solutions.

Use webmath.com
its awesome... you just type in the equation ( under finding a square) and it will do everything for you... even show you step by step / the "work" that you usually have to show teachers..
its neverrr wrong.

-2x^2 - 3x - 3 = 0
-2x^2 - 3x = 3
(-2x^2 - 3x)/(-2) = 3/(-2)
x^2 + 3x/2 = -3/2
x^2 + (3x/2)/2 + (3x/2)/2 = -3/2
x^2 + (3x/2)(1/2) + (3x/2)(1/2) = -3/2
x^2 + 3x/4 + 3x/4 + 9/16 = -3/2 + 9/16
(x^2 + 3x/4) + (3x/4 + 9/16) = -24/16 + 9/16
x(x + 3/4) + 3/4(x + 3/4) = -15/16
(x + 3/4)(x + 3/4) = -15/16
(x + 3/4)^2 = -15/16
x + 3/4 = ±√(-15/16)
x + 3/4 = ±√[(i^2 * 15)/4^2]
x + 3/4 = ±(i√15)/4
x = -3/4 ±(i√15)/4
x = (-3 ±i√15)/4

x=[3 + & - (9-24)^1/2]/-4
x is NOT a real no.

multiply the whole shebang by negative one to get 2x^2 + 3x + 3 = 0,
then look up how to complete the square. It's not hard . .I've just forgotten for the minute . .I think you take half of the '3' and square it,adding the resulting 9/4 to both sides 'forcing' a square . .but,as I aid,look it up and practice a few,so you don't end up like meeee . .