The problem asks us to factor the quadratic equation $x^2 - 49 = 0$ and find its solutions $x_1$ and $x_2$ such that $x_1 < x_2$.

1. Problem Description

The problem asks us to factor the quadratic equation $x^2 - 49 = 0$ and find its solutions $x_1$ and $x_2$ such that $x_1 < x_2$.

2. Solution Steps

We can factor the equation using the difference of squares formula:

$a^2 - b^2 = (a - b)(a + b)$

In our case, $a = x$ and $b = 7$, so the equation becomes:

$x^2 - 49 = x^2 - 7^2 = (x - 7)(x + 7) = 0$

To find the solutions, we set each factor equal to zero:

$x - 7 = 0$ or $x + 7 = 0$

Solving for $x$ gives us:

$x = 7$ or $x = -7$

We are given that $x_1 < x_2$, so we have $x_1 = -7$ and $x_2 = 7$.

3. Final Answer

$x_1 = -7$

$x_2 = 7$