Option C: [tex]$x=-3 \pm\sqrt{2}[/tex]
Solution:
Given equation is [tex]x^{2}+6 x+7=0[/tex].
This is a quadratic equation.
Here a = 1, b = 6, c = 7
To solve the given equation by quadratic formula,
[tex]$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Substitute the given values in the quadratic formula, we 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 \pm2 \sqrt{2}}{2 }[/tex]
[tex]$x=\frac{2(-3 \pm\sqrt{2})}{2 }[/tex]
2 in the numerator and denominator are cancelled.
[tex]$x=-3 \pm\sqrt{2}[/tex]
Option C is the correct answer.
