1. **State the problem:** We have a photograph with width $x$ inches and length $x + 3$ inches. The area is given by $x(x + 3)$ square inches. 2. **Write the equation for the area:** The area is 70 square inches, so: $$x(x + 3) = 70$$ 3. **Expand the equation:** $$x^2 + 3x = 70$$ 4. **Rewrite as a quadratic equation:** $$x^2 + 3x - 70 = 0$$ 5. **Use the quadratic formula:** For $ax^2 + bx + c = 0$, the solutions are: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Here, $a=1$, $b=3$, and $c=-70$. 6. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 3^2 - 4(1)(-70) = 9 + 280 = 289$$ 7. **Find the roots:** $$x = \frac{-3 \pm \sqrt{289}}{2} = \frac{-3 \pm 17}{2}$$ 8. **Evaluate both solutions:** - $x = \frac{-3 + 17}{2} = \frac{14}{2} = 7$ - $x = \frac{-3 - 17}{2} = \frac{-20}{2} = -10$ 9. **Interpret the solutions:** Width $x$ must be positive, so $x = 7$ inches. 10. **Find the length:** $$\text{Length} = x + 3 = 7 + 3 = 10$$ inches. **Final answer:** The length of the photograph is 10 inches.