Final answer:
To solve the quadratic inequality x^(2)-5x-14>=0, we can apply the quadratic formula to find the solutions of the quadratic equation x^2 - 5x - 14 = 0. The solutions are x = 7 and x = -2. Therefore, the solution to the inequality x^(2)-5x-14>=0 is x ≥ 7 or x ≤ -2.
Step-by-step explanation:
To solve the quadratic inequality x^(2)-5x-14>=0, we can first factorize the quadratic expression if possible. However, in this case, the quadratic does not readily factorize. Therefore, we can apply the quadratic formula to find the solutions of the quadratic equation x^2 - 5x - 14 = 0. The quadratic formula is x = (-b ± √(b^2 - 4ac))/(2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -5, and c = -14. Substituting these values into the quadratic formula gives us the solutions x = (-(-5) ± √((-5)^2 - 4(1)(-14)))/(2(1)). Solving this equation yields x = (5 ± √(25 + 56))/2, which simplifies to x = (5 ± √81)/2. The solutions are x = (5 ± 9)/2, which further simplifies to x = 7 and x = -2. Therefore, the solution to the inequality x^(2)-5x-14>=0 is x ≥ 7 or x ≤ -2.