Question 134075
{{{x^2+6x+2=0}}}


Step 1: Move the constant term to the right hand side of the equation:


{{{x^2+6x=-2}}}


Step 2: Divide the coefficient on the 1st degree term by 2


{{{6/2=3}}}


Step 3: Square the result of Step 2:


{{{3^2=9}}}


Step 4:  Add the result of Step 3 to both sides of the equation:


{{{x^2+6x+9=-2+9}}}
{{{x^2+6x+9=7}}}


Step 5:  The left side of the equation is now a perfect square, so factor it:


{{{(x+3)^2=7}}}


Step 6:  Take the square root of both sides, remembering to consider both the positive and negative roots:


{{{x+3=sqrt(7)}}} or {{{x+3=-sqrt(7)}}}


Step 7: Isolate x:


{{{x=-3+sqrt(7)}}} or {{{x=-3-sqrt(7)}}}


Step 8: Check your answers


{{{(-3+sqrt(7))^2+6(-3+sqrt(7))+2=9-6*sqrt(7)+7-18+6*sqrt(7)+2=0}}}


{{{(-3-sqrt(7))^2+6(-3-sqrt(7))+2=9+6*sqrt(7)+7-18-6*sqrt(7)+2=0}}}