Final answer:
To solve the equation x² = 169, recognize it as a perfect square and take the square root of both sides, obtaining the solutions x = 13 and x = -13.
Step-by-step explanation:
To solve the equation x² = 169 using factoring, we look for two identical factors of 169 since the equal sign suggests that the product of these factors equals 169. The number 169 is a perfect square because it is 13 times 13, or 13². Therefore, the two factors of 169 that we need are ± 13. We can express this realization as x = ± 13.
The process of solving begins with recognizing that x² = 169 is already a perfect square. This means we simply take the square root of both sides of the equation. The square root of x² is x, and the square root of 169 is 13. However, we must consider both the positive and negative square roots, which gives us two solutions: x = 13 and x = -13.
Therefore, the solutions to the equation x² = 169 are x = 13 and x = -13, both of which satisfy the original equation when substituted back in. This process of solving quadratics by finding square roots is often quicker and simpler than using the quadratic formula, especially when the equation is already in the form of a perfect square.