Question

solve $3x^2 + 6x + 3 = 0$ using any method.

$x = \square$

Explanation:

Step1: Simplify the equation

Divide the entire equation \(3x^{2}+6x + 3 = 0\) by 3. We get \(x^{2}+2x + 1=0\).

Step2: Factor the quadratic

Notice that \(x^{2}+2x + 1\) is a perfect square trinomial, which factors as \((x + 1)^{2}=0\).

Step3: Solve for x

Take the square root of both sides: \(x+1 = 0\), so \(x=- 1\). Since the equation is a perfect square, there is a repeated root.

Answer:

\(x=-1\) (with multiplicity 2)