Solve the quadratic equation by completing the square. \[ x^{2}+6 x+4=0 \] First, choose the appropriate form and fill in the blanks with the correct numbers, Then, solve the equation. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. Form: \[ \begin{array}{l}(x+\square)^{2} \\ \text { Solution: }\end{array} \] \( x=\square \)

To solve the quadratic equation \( x^{2} + 6x + 4 = 0 \) by completing the square, follow these steps: ### Step 1: Arrange the Equation First, move the constant term to the other side: \[ x^{2} + 6x = -4 \] ### Step 2: Complete the Square 1. **Find Half of the Coefficient of \( x \):** \[ \frac{6}{2} = 3 \] 2. **Square This Value:** \[ 3^{2} = 9 \] 3. **Add and Subtract This Square Inside the Equation:** \[ x^{2} + 6x + 9 = -4 + 9 \] \[ (x + 3)^{2} = 5 \] ### Step 3: Solve for \( x \) 1. **Take the Square Root of Both Sides:** \[ x + 3 = \pm \sqrt{5} \] 2. **Isolate \( x \):** \[ x = -3 \pm \sqrt{5} \] ### Completed Form \[ \begin{array}{l}(x + 3)^{2} \\ \text{Solution: }\end{array} \] \( x = -3 + \sqrt{5}, x = -3 - \sqrt{5} \) ### Final Answer \[ \begin{array}{l}(x + 3)^{2} \\ \text{Solution: }\end{array} \] \( x = -3 + \sqrt{5},\, x = -3 - \sqrt{5} \)