How do you solve 6x² plus 6x plus 6 by completing the square?

Answer 1

You can't SOLVE something unless it's an EQUATION. So let's assume you mean the equation

6x² plus 6x plus 6 equals zero (a standard form for equations)

6x² + 6x + 6 = 0

same as

x² + x + 1 = 0 (div both sides by 6)

so

x² + x = -1

Now we can complete the square on THAT thing

x² + x + 1/2 = -1 + 1/2

(x + 1/2)2 = -1/2

Take square root of both sides:

x + 1/2 = √(-1/2)

And, sorry, but you're left with the square root of a negative number.

Have you learned about i, the "imaginary number" equal to the square root of negative 1? Because the right side of your equation is i over √2

Answer 2

6x2 + 6x + 6 is an expression, not an equality nor inequality, and so there is nothing that can be solved. Also, the discriminant is negative and so the corresponding equation has no real solutions. All that can be said is:6x2 + 6x + 6 = 6(x2 + x + 1) = 6[(x + 1/2)2 - 1/4 + 1] = 6*[(x + 1/2)2 + 3/4].