Question

Solve for x. x2+6x+6=0 Enter your answers in the boxes. x = or x =

Answer 1

`x=-3+√(3)\text{ or }x=-3-√(3)`

Step-by-step explanation:

The equation is
`x^2+6x+6=0` .

I will complete squares to solve for x.

`\text{Given: }x^2+6x+6=0\\ \\ \text{Subtract 6 from both sides: }x^2+6x=-6\\ \\ \text{Add the square of the half of the coefficient of x to both sides:}\\\\ \text{ }x^2+6x+9=-6+9`

`\text{Factor the left side and simplify the right side: }(x+3)^2=3`

`\text{Square root both sides: }x+3=\pm √(3)`

`\text{Clear x:}\\ \\ x=-3\pm √(3)\\\\ x=-3-√(3)\text{ or }x=-3+√(3)`