When the square of a number is added to six times the number the result is 56. What is the number?

Let the number be ( x ). The equation can be set up as ( x^2 + 6x = 56 ). Rearranging gives ( x^2 + 6x - 56 = 0 ). Factoring the quadratic, we find ( (x + 14)(x - 4) = 0 ), leading to the solutions ( x = -14 ) and ( x = 4 ). Thus, the number is 4.