Question

how many real solutions does the equation have?
(x^2 - 25 = 0)
2 real solutions
one real solution
78 real solutions

Explanation:

Step1: Analyze the equation type

The equation given is \(x^{2}-25 = 0\), which is a quadratic equation in the form \(ax^{2}+bx + c=0\) (here \(a = 1\), \(b = 0\), \(c=- 25\)). We can also solve it by factoring or using the square - root property.

Step2: Solve the equation

We can rewrite the equation \(x^{2}-25 = 0\) as \(x^{2}=25\). By the square - root property, if \(x^{2}=k\) (\(k\geq0\)), then \(x=\pm\sqrt{k}\). For \(k = 25\), we have \(x=\pm\sqrt{25}=\pm5\). So the solutions are \(x = 5\) and \(x=-5\).

Step3: Determine the number of real solutions

Since we found two distinct real values (\(5\) and \(- 5\)) that satisfy the equation \(x^{2}-25 = 0\), the number of real solutions is 2.

Answer:

The equation \(x^{2}-25 = 0\) has 2 real solutions.