Answer
The solutions are $x\approx 0.74$ and $x\approx -6.74$.
Work Step by Step
The given equation is
$\Rightarrow x^2+6x=5$
The coefficient of the $x^2-$term is $1$, and the coefficient of the $x-$term is an even number.
So, solve by completing the square.
$\Rightarrow x^2+6x=5$
Add $(\frac{b}{2})^2=(\frac{6}{2})^2=9$ to each side.
$\Rightarrow x^2+6x+9=5+9$
Write the left side as the square of a binomial.
$\Rightarrow (x+3)^2=14$
Take the square root of each side.
$\Rightarrow x+3=\pm\sqrt{14}$
Subtract $3$ from each side.
$\Rightarrow x+3-3=-3\pm\sqrt{14}$
Simplify.
$\Rightarrow x=-3\pm\sqrt{14}$
The solutions are $x=-3+\sqrt{14}\approx 0.74$ and $x=-3-\sqrt{14}\approx -6.74$.
