Question

what are the solution(s) to the quadratic equation $x^2 - 25 = 0$?
○ $x = 5$ and $x = -5$
○ $x = 25$ and $x = -25$
○ $x = 125$ and $x = -125$
○ no real solution

Explanation:

Step1: Isolate \(x^2\)

We start with the equation \(x^2 - 25 = 0\). To isolate \(x^2\), we add 25 to both sides of the equation.
\[x^2 - 25 + 25 = 0 + 25\]
\[x^2 = 25\]

Step2: Take square root of both sides

Now, we take the square root of both sides. Remember that if \(x^2 = a\) (where \(a\geq0\)), then \(x=\pm\sqrt{a}\). Here, \(a = 25\), so:
\[x=\pm\sqrt{25}\]
Since \(\sqrt{25}=5\), we have:
\[x = 5 \text{ or } x=-5\]

Answer:

A. \(x = 5\) and \(x = -5\)