Answer:
[tex]x=-3-\sqrt{2}[/tex] or [tex]x=-3+\sqrt{2}[/tex]
Step-by-step explanation:
The given equation is
[tex]x^2+6x+7=0[/tex]
Comparing to [tex]ax^2+bx+c=0[/tex], we have a=1,b=6,d=7
The solution to this equation can be obtained using the quadratic formula;
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Plug in the values to get;
[tex]x=\frac{-6\pm \sqrt{6^2-4(1)(7)} }{2(1)}[/tex]
[tex]x=\frac{-6\pm \sqrt{36-28} }{2}[/tex]
[tex]x=\frac{-6\pm \sqrt{8} }{2}[/tex]
[tex]x=\frac{-6\pm 2\sqrt{2} }{2}[/tex]
[tex]x=-3-\sqrt{2}[/tex] or [tex]x=-3+\sqrt{2}[/tex]
Answer:
[tex]x=-3+\sqrt{2}\text{ and }x=-3-\sqrt{2}[/tex]
Step-by-step explanation:
Given quadratic equation,
[tex]x^2 + 6x + 7 = 0[/tex]
By quadratic formula,
[tex]x=\frac{-6\pm \sqrt{6^2-4\times 1\times 7}}{2\times }[/tex]
[tex]=\frac{-6\pm \sqrt{36-28}}{2}[/tex]
[tex]=\frac{-6\pm \sqrt{8}}{2}[/tex]
[tex]=\frac{-6\pm 2\sqrt{2}}{2}[/tex]
[tex]=-3\pm \sqrt{2}[/tex]
[tex]\implies x=-3+\sqrt{2}\text{ or }x=-3-\sqrt{2}[/tex]
Hence, the solution of the given equation are,
[tex]x=-3+\sqrt{2}\text{ and }x=-3-\sqrt{2}[/tex]
