The given expression is:
[tex] x^{2} +6x=-7 \\ \\
x^{2} +2(x)(3)=-7[/tex]
Adding the square of 3 to both sides, to make the left hand side of the equation a complete square, we get:
[tex] x^{2} +2(x)(3)+ 3^{2}=-7+ 3^{2} \\ \\
(x+3)^{2}=2 \\ \\
x+3=+- \sqrt{2}
[/tex]
So the values of x are:
a) [tex]x= \sqrt{2} - 3 = -1.59[/tex]
b) [tex]x= -\sqrt{2} - 3 = -4.41[/tex]
