Solve the quadratic equation using completing the square. \[ 2 p^{2}+12 p-14=0 \]

To solve the quadratic equation \( 2p^{2}+12p-14=0 \) by completing the square, we first divide all terms by 2 to simplify: \[ p^{2} + 6p - 7 = 0 \] Now, isolate the constant term: \[ p^{2} + 6p = 7 \] Next, we complete the square. Take half of the coefficient of \( p \), which is 6, and square it: \[ \left(\frac{6}{2}\right)^{2} = 3^{2} = 9 \] Adding 9 to both sides gives: \[ p^{2} + 6p + 9 = 7 + 9 \] This simplifies to: \[ (p + 3)^{2} = 16 \] Taking the square root of both sides results in: \[ p + 3 = \pm 4 \] Now, solve for \( p \): 1. \( p + 3 = 4 \) leads to \( p = 1 \) 2. \( p + 3 = -4 \) leads to \( p = -7 \) Thus, the solutions to the equation are: \[ p = 1 \quad \text{and} \quad p = -7 \]