Question

Solve for x . x^2+6x+6=0

Answer 1

`\boxed {x = √(3) - 3}`

`\boxed {x = -√(3) - 3}`

Explanation:

Solve for the value of
`x`:

`x^2 + 6x + 6 = 0`

-When you use the quadratic formula (
`\frac{-b\pm \sqrt{b^(2) - 4ac}}{2a}` ), it would give you two solutions. So, use the quadratic formula:

`x = \frac{-6\pm \sqrt{6^(2) - 4 * 6}}{2}`

-Simplify
`6` by the exponent
`2`:

`x = \frac{-6\pm \sqrt{6^(2) - 4 * 6}}{2}`

`x = (-6\pm √(36 - 4 * 6))/(2)`

-Multiply both
`-4` and
`6`:

`x = (-6\pm √(36 - 4 * 6))/(2)`

`x = (-6\pm √(36 - 24))/(2)`

-Add
`34` and
`-24`:

`x = (-6\pm √(36 - 24))/(2)`

`x = (-6\pm √(12))/(2)`

-Take the square root of
`12`:

`x = (-6\pm √(12))/(2)`

`x = (-6\pm 2√(3))/(2)`

-Now solve the equation when
`\pm` is plus, So, add
`-6` to
`2√(3)`:

`x = (-6\pm 2√(3))/(2)`

`x = (2√(3) - 6)/(2)`

-Divide
`-6 + 2√(3)` both sides by
`2`:

`x = (2√(3) - 6)/(2)`

`\boxed {x = √(3) - 3}` (Answer 1)

-Now solve the equation when
`\pm` is minus. So, Subtract
`2√(3)` from
`-6`:

`x = (-2√(3) - 6)/(2)`

-Divide
`-2√(3) - 6` by
`2`:

`x = (-2√(3) - 6)/(2)`

`\boxed {x = -√(3) - 3}` (Answer 2)