Solve by completing the square please, and could you show all the steps.?

Add 9 to both sides of the equation:

-2x² - 12x = 9

Divide both sides by -2:

x² + 6x = -9/2

Add a² to both sides of the equation:

x² + 6x + a² = -9/2 + a²

Using the pattern (x + a)² = x² + 2ax + a², we see that we can solve for "a" by setting the middle term in the pattern equal to the middle term in the equation:

2ax = 6x

a = 3

a² = 9

x² + 6x + 9 = -9/2 + 9

We know that the left side is the square of x + 3:

(x + 3)² = 9/2

Take the square root of both sides:

x + 3 = ±3√2/2

x = -3 ± 3√2/2

- 2 (x² + 6x) = 9

- 2 (x² + 6x + 9) = 9 - 18

- 2 [ x + (3/2) ]² = - 9

[ x + (3/2) ]² = 9/2

x + (3/2) = ± 3 / √2

x = - (3/2) ± 3 /√2

this link has a step by step solution to your problem:

https://www.symbolab.com/solver/step-by-step/-2x%5...

hope it helps