Final answer:
To find the positive solution, we can solve the quadratic equation x^2 - 5x - 36 = 0 by factoring.
Step-by-step explanation:
To solve the problem, let's represent the number in question as 'x'. The problem states that when 36 is subtracted from the square of the number 'x', the result is 5 times the number 'x'. We can write this as an equation: x^2 - 36 = 5x. To find the positive solution, we can solve this quadratic equation.
By rearranging the equation, we get x^2 - 5x - 36 = 0. To factorize the quadratic equation, we need to find two numbers whose product is -36 and whose sum is -5. The numbers that satisfy this are -9 and 4. Therefore, the equation factors to (x - 9)(x + 4) = 0. Setting each factor equal to zero, we find the two possible solutions: x - 9 = 0 or x + 4 = 0. From this, we find that x = 9 or x = -4.
Since we are looking for the positive solution, the answer is x = 9.