To solve the quadratic equation \(x^2 - 13x + 12 = 0\), we can factor it.
We need to find two numbers that multiply to \(12\) (the constant term) and add up to \(-13\) (the coefficient of \(x\)).
The numbers that satisfy these conditions are \(-1\) and \(-12\), since:
\[ -1 \times -12 = 12 \] \[ -1 + (-12) = -13 \]
Therefore, we can factor the equation as follows:
\[ (x - 1)(x - 12) = 0 \]
Setting each factor equal to zero gives us:
\[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \] \[ x - 12 = 0 \quad \Rightarrow \quad x = 12 \]
Thus, the solutions to the equation are \(x = 1\) and \(x = 12\).
The correct answer is:
D. x = 12 and x = 1