To solve the equation \( x^2 - 11x + 30 = 0 \), we can use the factoring method.
- We need to factor the quadratic equation. We are looking for two numbers that multiply to 30 (the constant term) and add up to -11 (the coefficient of the linear term).
The two numbers that meet these criteria are -5 and -6, since:
\[ -5 \times -6 = 30 \] \[ -5 + -6 = -11 \]
- Now, we can write the equation in its factored form:
\[ (x - 5)(x - 6) = 0 \]
- To find the values of \( x \), we set each factor equal to zero:
\[ x - 5 = 0 \quad \text{or} \quad x - 6 = 0 \]
- Solving these equations gives:
\[ x = 5 \quad \text{or} \quad x = 6 \]
Thus, the solutions to the equation \( x^2 - 11x + 30 = 0 \) are:
\[ \boxed{5} \quad \text{and} \quad \boxed{6} \]