Question

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

Answer 1

Option C: $x=-3 \pm\sqrt{2}$

Solution:

Given equation is $x^{2}+6 x+7=0$.

This is a quadratic equation.

Here a = 1, b = 6, c = 7

To solve the given equation by quadratic formula,

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

Substitute the given values in the quadratic formula, we get

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

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

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

$x=\frac{-6 \pm2 \sqrt{2}}{2 }$

$x=\frac{2(-3 \pm\sqrt{2})}{2 }$

2 in the numerator and denominator are cancelled.

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

Option C is the correct answer.