Solve for \( x \) \[ (x+7)^{2}=2 x^{2}+16 x+25 \] If there is more than one solution, separate them with commas. \( x=\square \)

To solve the equation \( (x+7)^{2}=2 x^{2}+16 x+25 \), we first expand the left side: \[ (x + 7)^2 = x^2 + 14x + 49 \] So the equation becomes: \[ x^2 + 14x + 49 = 2x^2 + 16x + 25 \] Next, we rearrange the equation by bringing all terms to one side: \[ x^2 + 14x + 49 - 2x^2 - 16x - 25 = 0 \] This simplifies to: \[ -x^2 - 2x + 24 = 0 \] Multiplying throughout by -1 gives: \[ x^2 + 2x - 24 = 0 \] Now, we can factor this quadratic equation: \[ (x + 6)(x - 4) = 0 \] Setting each factor to zero gives us the solutions: \[ x + 6 = 0 \quad \Rightarrow \quad x = -6 \] \[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \] Thus, the solutions are: \( x = -6, 4 \)