Final answer:
The quadratic equation k² - 7k - 18 = 0 is factored into (k - 9)(k + 2) = 0, yielding two solutions: k = 9 and k = -2.
Step-by-step explanation:
To solve the quadratic equation k² - 7k - 18 = 0, you can use the factoring method, as this is a quadratic equation of the form ax² + bx + c = 0. The equation factors to (k - 9)(k + 2) = 0. Setting each factor equal to zero gives k - 9 = 0 or k + 2 = 0, which leads to two solutions for k.
- k - 9 = 0 → k = 9
- k + 2 = 0 → k = -2
Therefore, the solutions to the equation are k = 9 and k = -2. It is always a good practice to check these solutions by substituting them back into the original equation to ensure that they satisfy the equation.