the product of two positive numbers is 750. the first number is 5 less than the second number. the equation…

Explanation:

Step1: Expand the equation

Expand $x(x - 5)=750$ to get $x^{2}-5x - 750=0$.

Step2: Factor the quadratic equation

We factor $x^{2}-5x - 750=0$. We need two numbers that multiply to - 750 and add up to - 5. The numbers are - 30 and 25. So, $(x - 30)(x + 25)=0$.

Step3: Solve for x

Set each factor equal to zero: $x-30 = 0$ gives $x = 30$; $x + 25=0$ gives $x=-25$. Since we are looking for positive numbers, we discard $x=-25$.

Answer:

C. 30