4x+x2=0

Treat as a quadratic in x: x^2 + 4x = 0.

• Factor: x(x + 4) = 0
• Zeros: x = 0 or x = -4

Check:

• x = 0 → 0
• x = -4 → (-4)^2 + 4(-4) = 16 - 16 = 0

Alternative methods:

• Completing the square: (x + 2)^2 = 4 → x = 0, -4
• Quadratic formula: x = [-4 ± sqrt(16)]/2 → x = 0, -4

Answer: x = 0 or x = -4.