Solve the equation given by completing the square. \( 5 x^{2}+30 x+25=0 \) [Hint: Divide by 5 first] \( x=\square \)

To solve the equation \( 5x^{2} + 30x + 25 = 0 \) by completing the square, follow these steps: 1. **Divide the entire equation by 5** to simplify: \[ x^{2} + 6x + 5 = 0 \] 2. **Move the constant term to the other side**: \[ x^{2} + 6x = -5 \] 3. **Complete the square**: - Take half of the coefficient of \( x \), which is \( 6/2 = 3 \). - Square it: \( 3^2 = 9 \). - Add 9 to both sides of the equation: \[ x^{2} + 6x + 9 = -5 + 9 \] \[ (x + 3)^2 = 4 \] 4. **Take the square root of both sides**: \[ x + 3 = \pm 2 \] 5. **Solve for \( x \)**: - When using the positive square root: \[ x + 3 = 2 \implies x = -1 \] - When using the negative square root: \[ x + 3 = -2 \implies x = -5 \] **Final Solutions:** \[ x = -1 \quad \text{and} \quad x = -5 \]