Final answer:
To solve the quadratic inequality x2 - 5x - 35 ≥ 15, we first subtract 15 from both sides to get x2 - 5x - 50 ≥ 0. Then, we factor the quadratic expression and find its zeros: (x - 10)(x + 5) ≥ 0. This inequality is satisfied when either both factors are nonnegative or both factors are negative. Therefore, the solution set is x ≤ -5 or x ≥ 10.
Step-by-step explanation:
To solve the quadratic inequality x^2 - 5x - 35 ≥ 15, we first subtract 15 from both sides to get x^2 - 5x - 50 ≥ 0. Then, we factor the quadratic expression and find its zeros: (x - 10)(x + 5) ≥ 0. This inequality is satisfied when either both factors are nonnegative or both factors are negative. Therefore, the solution set is x ≤ -5 or x ≥ 10.