Final answer:
The value of the expression \(\sqrt{x^2 + 12} + |b|\) when \(b = 14\) is \(\sqrt{x^2 + 12} + 14\), but the value of \(x\) is needed to calculate a specific numerical answer.
Step-by-step explanation:
The question asks for the value of the expression \(\sqrt{x^2 + 12} + |b|\) when \(a = -2\) and \(b = 14\). The given values of \(a\) and \(b\) have to be plugged into the expression to find its value. However, the given expression does not contain the variable \(a\), so the value of \(a = -2\) is irrelevant for this particular question. Thus, we only need to focus on the value of \(b\) which is \(14\).
The absolute value of \(b\), denoted as \(|b|\), is simply the non-negative value of \(b\). Since \(b = 14\), \(|b| = 14\). The first part of the expression, \(\sqrt{x^2 + 12}\), will depend on the value of \(x\). However, since the value of \(x\) wasn't provided in the question, we cannot give a numerical value for this part of the expression.
In conclusion, the value of the original expression, given the value of \(b = 14\) but without knowing the value of \(x\), is \(\sqrt{x^2 + 12} + 14\).