Answer
$x = (−3-\sqrt 7, −3+\sqrt 7)$
Work Step by Step
Step-1 : Subtract $2$ from both sides of the equation
$x^2+6x=-2$
Step -2 : Add the square of half of the co-efficient of $x$ to both sides.
Co-efficient of $x = 6$
Half of $6 = \frac{1}{2}×6=3$
Square of $3$ is $3×3=9$
The equation becomes $x^2+6x+9=-2+9$
Step-3 Factor the trinomial and simplify the right hand side.
$(x+3)^2=7$
Step-4 Use the square root property and solve for $x$
$(x+3)=±\sqrt 7$
Step-5 Subtract 3 on both the sides
$x=−3±\sqrt 7$
Therefore the solution set is $(−3-\sqrt 7, −3+\sqrt 7)$
