Solve each equation by completing the square 1) \( p^{2}+14 p-38=0 \) 3) \( a^{2}+14 a-51=0 \) 5) \( x^{2}+6 x+8=0 \) 7) \( x^{2}+14 x-15=0 \) 5 ( 150

Completing the square for \( p^{2}+14p-38=0 \) involves moving -38 to the other side, giving \( p^{2}+14p=38 \). Next, take half of the coefficient of \( p \) (which is 14), square it (that’s 49), and add it to both sides, resulting in \( (p+7)^{2}=87 \). Solving for \( p \) gives two solutions: \( p = -7 + \sqrt{87} \) and \( p = -7 - \sqrt{87} \). For \( a^{2}+14a-51=0 \), we adjust to find \( a^{2}+14a=51 \). Following the same steps, we add \( 49 \) to both sides, leading to \( (a+7)^{2}=100 \). This gives us \( a = -7 + 10 \) and \( a = -7 - 10 \), or simplified solutions: \( a = 3 \) and \( a = -17 \).