Final answer:
To find the positive solution of the equation representing '5 times a number is 14 less than the square of that number,' we use the quadratic formula. The positive solution obtained is 7, which corresponds to option A.
Step-by-step explanation:
The problem given is "5 times a number is 14 less than the square of that number." Let's call the number x. The equation based on this problem is 5x = x² - 14. To solve for x, we must rearrange this into the standard form of a quadratic equation: x² - 5x - 14 = 0. Applying the quadratic formula x = [-b ± √(b² - 4ac)] / (2a), where a = 1, b = -5, and c = -14, we get x = (5 ± √(25 + 56)) / 2. Simplifying, x = (5 ± √81) / 2 gives us two solutions, x = (5 + 9) / 2 = 7 and x = (5 - 9) / 2 = -2. However, only the positive solution is requested, thus x = 7 is the answer, which corresponds to option A.