A photograph has a length that is 2 inches longer than its width, x. So its area is given by the expression x(x+2) square inches. If the area of the photograph is 48 square inches, what is the width of the photograph? The width of the photograph is __ inches. The solution is square

To find the width of the photograph, we need to solve the equation $x(x+2) = 48$ for $x$.<br /><br />Step 1: Expand the equation<br />$x^2 + 2x = 48$<br /><br />Step 2: Move all terms to one side of the equation<br />$x^2 + 2x - 48 = 0$<br /><br />Step 3: Factor the quadratic equation<br />$(x + 8)(x - 6) = 0$<br /><br />Step 4: Set each factor equal to zero and solve for $x$<br />$x + 8 = 0$ or $x - 6 = 0$<br />$x = -8$ or $x = 6$<br /><br />Since the width of the photograph cannot be negative, we discard the solution $x = -8$.<br /><br />Therefore, the width of the photograph is 6 inches.<br /><br />The solution is 6.