1. The problem is to simplify the expression $-43 + (x - 6)^2$. 2. The formula for squaring a binomial is $ (a - b)^2 = a^2 - 2ab + b^2 $. 3. Applying this to $ (x - 6)^2 $, we get: $$ (x - 6)^2 = x^2 - 2 \times x \times 6 + 6^2 = x^2 - 12x + 36 $$ 4. Substitute back into the original expression: $$ -43 + (x - 6)^2 = -43 + x^2 - 12x + 36 $$ 5. Combine like terms: $$ -43 + 36 = -7 $$ 6. So the simplified expression is: $$ x^2 - 12x - 7 $$ This is the final simplified form of the expression.