Question

Solve x2 + 6x + 7 = 0. (2 points)

Answer 1

`x=-3+√(2)\text{ and }x=-3-√(2)`

Explanation:

Given quadratic equation,

`x^2 + 6x + 7 = 0`

By quadratic formula,

`x=(-6\pm √(6^2-4* 1* 7))/(2* )`

`=(-6\pm √(36-28))/(2)`

`=(-6\pm √(8))/(2)`

`=(-6\pm 2√(2))/(2)`

`=-3\pm √(2)`

`\implies x=-3+√(2)\text{ or }x=-3-√(2)`

Hence, the solution of the given equation are,

`x=-3+√(2)\text{ and }x=-3-√(2)`

Answer 2

`x=-3-√(2)` or
`x=-3+√(2)`

Explanation:

The given equation is

`x^2+6x+7=0`

Comparing to
`ax^2+bx+c=0`, we have a=1,b=6,d=7

The solution to this equation can be obtained using the quadratic formula;

`x=(-b\pm √(b^2-4ac) )/(2a)`

Plug in the values to get;

`x=(-6\pm √(6^2-4(1)(7)) )/(2(1))`

`x=(-6\pm √(36-28) )/(2)`

`x=(-6\pm √(8) )/(2)`

`x=(-6\pm 2√(2) )/(2)`

`x=-3-√(2)` or
`x=-3+√(2)`