Solve.xsquaredminus11xplus30equals0Question content area bottomPart 1Select the correct choice below and fill in any answer boxes within your choice.

1 answer

To solve the equation \( x^2 - 11x + 30 = 0 \), we can use the factoring method.

  1. 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:

\[ -5 \times -6 = 30 \] \[ -5 + -6 = -11 \]

  1. Now, we can write the equation in its factored form:

\[ (x - 5)(x - 6) = 0 \]

  1. To find the values of \( x \), we set each factor equal to zero:

\[ x - 5 = 0 \quad \text{or} \quad x - 6 = 0 \]

  1. Solving these equations gives:

\[ x = 5 \quad \text{or} \quad x = 6 \]

Thus, the solutions to the equation \( x^2 - 11x + 30 = 0 \) are:

\[ \boxed{5} \quad \text{and} \quad \boxed{6} \]