When an equation involves a squared variable expression set equal to a numeric expression, the analysis of solutions depends on the value of the numeric expression.
1. If the numeric expression is zero (for example, if the equation is \( x^2 = 0 \)), then there is indeed **one solution**, which is \( x = 0 \).
2. If the numeric expression is a positive number (for instance, \( x^2 = 4 \)), there will be two solutions (e.g., \( x = 2 \) and \( x = -2 \)).
3. If the numeric expression is negative (e.g., \( x^2 = -1 \)), there are no real solutions since a square cannot equal a negative number.
Given these points, the correct statement in the context of the provided options is:
**If the numeric expression is zero, there is one solution.**