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Evaluate the following algebraic expression for the given value of .
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Identify the given algebraic expression and the value of the variable. Here, the expression is \(x^2 + 4x + 6\) and the value given is \(x = -2\).
Substitute the value of \(x\) into the expression. Replace every \(x\) in the expression with \(-2\), so the expression becomes \((-2)^2 + 4(-2) + 6\).
Evaluate each term separately: calculate \((-2)^2\), then calculate \(4 \times (-2)\), and keep the constant term \(6\) as is.
Add the results of the evaluated terms together: the value from \((-2)^2\), plus the value from \(4(-2)\), plus \(6\).
Combine the sums to find the final value of the expression after substitution.