The difference between a negative integer and its square is 6 fewer than twice that integer. What is the integer?

Answer 1

x - x² = 2x - 6

x² + x - 6 = 0

(x - 2)(x + 3) = 0

x = 2 or x = - 3. The condition that x be - means the integer is -3.

Check: -3 - (-3)² =? 2(-3) - 6. - 12 = - 12