Final answer:
To solve the equation x^2 - 40 = 3x, we rearranged it to x^2 - 3x - 40 = 0 and applied the quadratic formula. The positive solution of the equation is approximately x ~ 7.37.
Step-by-step explanation:
When faced with the problem "When 40 is subtracted from the square of a number, the result is 3 times the number", we are looking for the number that satisfies this condition. To find it, we can set up an equation based on the given information:
x^2 - 40 = 3x.
This is a quadratic equation, which can be rearranged to standard form:
x^2 - 3x - 40 = 0.
To solve for x, we can apply the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a = 1, b = -3, and c = -40.
After plugging the values into the formula, we get two solutions. However, since we are looking for the positive solution, we discard the negative one and find that the positive solution is x ~ 7.37. This is the number that when squared and reduced by 40 gives a result of three times the number itself.