What is the solution set for x^2+6x+9=0 ? -6 -3 6 9

To solve the quadratic equation \(x^2 + 6x + 9 = 0\), we can use factoring, completing the square, or the quadratic formula. In this case, the equation can be factored easily.<br /><br />First, we recognize that the quadratic can be written as a perfect square trinomial:<br />\[ x^2 + 6x + 9 = (x + 3)^2 \]<br /><br />So, the equation becomes:<br />\[ (x + 3)^2 = 0 \]<br /><br />To solve for \(x\), we take the square root of both sides:<br />\[ x + 3 = 0 \]<br /><br />Solving for \(x\):<br />\[ x = -3 \]<br /><br />Therefore, the solution set is:<br />\[ \{ -3 \} \]<br /><br />So, the correct answer is:<br />\[ \{ -3 \} \]