Question

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

Answer 1

Answer:

$x=-3+\sqrt{2}\text{ and }x=-3-\sqrt{2}$

Step-by-step explanation:

Given quadratic equation,

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

By quadratic formula,

$x=\frac{-6\pm \sqrt{6^2-4\times 1\times 7}}{2\times }$

$=\frac{-6\pm \sqrt{36-28}}{2}$

$=\frac{-6\pm \sqrt{8}}{2}$

$=\frac{-6\pm 2\sqrt{2}}{2}$

$=-3\pm \sqrt{2}$

$\implies x=-3+\sqrt{2}\text{ or }x=-3-\sqrt{2}$

Hence, the solution of the given equation are,

$x=-3+\sqrt{2}\text{ and }x=-3-\sqrt{2}$

Answer 2

Answer:

$x=-3-\sqrt{2}$ or $x=-3+\sqrt{2}$

Step-by-step 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;

$x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}$

Plug in the values to get;

$x=\frac{-6\pm \sqrt{6^2-4(1)(7)} }{2(1)}$

$x=\frac{-6\pm \sqrt{36-28} }{2}$

$x=\frac{-6\pm \sqrt{8} }{2}$

$x=\frac{-6\pm 2\sqrt{2} }{2}$

$x=-3-\sqrt{2}$ or $x=-3+\sqrt{2}$