Question 144288
Solve by completing the square:
{{{x^2+6x+2 = 0}}} First, subtract 2 from both sides.
{{{x^2+6x = -2}}} Now complete the square in x by adding the square of half the x-coefficient ({{{(6/2)^2 = 9}}}) to both sides of the equation.
{{{x^2+6x+9 = -2+9}}} Simplify. Factor the left side.
{{{(x+3)(x+3) = 7}}}
{{{(x+3)^2 = 7}}} Now take the square root of both sides.
{{{x+3 = sqrt(7)}}} or {{{x+3 = -sqrt(7)}}} Finally, subtract 3.
{{{x = -3+sqrt(7)}}} or {{{x = -3-sqrt(7)}}}