$x^{2}-25=0$

Step 1 ：Given the quadratic equation \(x^{2}-25=0\).

Step 2 ：The general form of a quadratic equation is \(ax^{2}+bx+c=0\). In this case, a=1, b=0, and c=-25.

Step 3 ：The solutions to a quadratic equation are given by the formula \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).

Step 4 ：Substitute a=1, b=0, and c=-25 into the formula, we get \(x=\frac{-0\pm\sqrt{0^{2}-4*1*(-25)}}{2*1}\).

Step 5 ：Simplify the above expression, we get \(x=\frac{\pm\sqrt{100}}{2}\).

Step 6 ：Further simplify the above expression, we get \(x=\pm5\).

Step 7 ：\(\boxed{x = 5, x = -5}\) are the solutions to the equation \(x^{2}-25=0\).