The equation (x + p)^2 = q represents a quadratic relationship where x is a variable, p is a constant, and q is the result of squaring the sum of x and p. This means that when you add p to x and then square the result, you get q. To solve for x, you can first take the square root of both sides, leading to two possible equations: x + p = \sqrtq or x + p = -\sqrtq. From there, you can isolate x by subtracting p from both sides, giving you the solutions x = \sqrtq - p and x = -\sqrtq - p.