Solve the Quadratic Equation: x² - 25 = 0 Step by Step

To solve the equation $x^2 - 25 = 0$, follow these steps:

• Step 1: Isolate the square term: Begin by rewriting the equation to isolate $x^2$:

$x^2 - 25 = 0$
Add $25$ to both sides to obtain:
$x^2 = 25$

• Step 2: Extract the square roots: To solve $x^2 = 25$, take the square root of both sides. Remember to consider both the positive and negative roots:

$x = \pm \sqrt{25}$

• Step 3: Simplify: Calculate the square root of 25:

$\sqrt{25} = 5$

Therefore, the solutions are:
$x = 5$
and
$x = -5$

Thus, the solutions to the equation $x^2 - 25 = 0$ are $x_1 = 5$ and $x_2 = -5$.

Verifying with the provided choices, the correct choice matches the solution $x_1 = 5, x_2 = -5$.

Therefore, the solution to the problem is $x_1 = 5, x_2 = -5$.