### Instruction: What is the least integer whose square is 48 more than its double?### Response: I need to find an integer x such that x^2 = 2x + 48.
I can rearrange this equation to get x^2 - 2x - 48 = 0.
This is a quadratic equation, so I can try to factor it into two binomials.
I look for two numbers that multiply to -48 and add to -2.
I notice that -8 and 6 are such numbers, so I can write x^2 - 2x - 48 = (x - 8)(x + 6) = 0.
This means that either x - 8 = 0 or x + 6 = 0, so x = 8 or x = -6.
However, I only want the least integer, so I choose x = -6.