To solve the equation \(x^2 = 19\), we need to find the values of \(x\) that satisfy this equation. Since the equation is a quadratic equation, it will have two solutions. We can find these solutions by taking the square root of both sides of the equation. The solutions will be \(x = \pm \sqrt{19}\).
Step 1: Identify the Equation
We are given the equation \(x^2 = 19\). This is a quadratic equation, and we need to find the values of \(x\) that satisfy this equation.
Step 2: Solve the Equation
To solve the equation \(x^2 = 19\), we take the square root of both sides. This gives us two solutions because the square root function has both positive and negative roots.
Step 3: Express the Solutions
The solutions to the equation are:
\[ x = \pm \sqrt{19} \]
Final Answer
The solutions to the equation \(x^2 = 19\) are:
\[ \boxed{x = \pm \sqrt{19}} \]