Given that \( x=3 \) is a solution of the equation \( x^{2}+8 x+c=0 \)

To solve for \( c \) when \( x=3 \) is a solution of the equation \( x^{2}+8x+c=0 \), we can substitute \( x=3 \) into the equation. This gives us: \[ 3^{2} + 8(3) + c = 0 \] \[ 9 + 24 + c = 0 \] \[ 33 + c = 0 \] \[ c = -33 \] So, the value of \( c \) is \( -33 \). Now you can plug \( c \) back into the original equation to confirm that \( x=3 \) is indeed a solution! Fun fact: This approach is based on the principle of applying known roots to find coefficients in polynomial equations. It’s like piecing together a puzzle where you already have part of it completed!