The problem is a(a-c)=23. Solve for c if both a and c are positive numbers. Thanks

C must equal 22 and A must equal 23 since 23 is a prime number. So, 23(23-22)=23

To solve the equation a(a - c) = 23 for c, we need to isolate the variable c. Here's how we can do it step by step:

1. Expand the expression: a(a - c) = 23
This gives us: a^2 - ac = 23

2. Rearrange the equation to isolate the term with the variable c:
Subtract 23 from both sides of the equation: a^2 - ac - 23 = 0

3. Now, we have a quadratic equation in terms of a. To solve for c, we can either factorize or use the quadratic formula. However, since finding factors of 23 might not yield a whole number solution, we'll use the quadratic formula.

The quadratic formula is given as: x = (-b ± √(b^2 - 4ac)) / 2a

In this case, our variables are:
- x = c
- a = 1
- b = -a
- c = -23

Plugging in these values into the quadratic formula, we get:
c = (-(-a) ± √((-a)^2 - 4 * 1 * (-23))) / (2 * 1)

4. Simplify the equation:
c = (a ± √(a^2 + 92)) / 2

Now, since both a and c are positive numbers, we can eliminate the negative root and only consider the positive root:
c = (a + √(a^2 + 92)) / 2

This is the solution for c in terms of a. Depending on the value of a, you can evaluate c using this formula.