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The solutions are \(x=-4\) and \(x=4\).
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Beyond the Answer
To solve the equation \( 2x - 16 = x(2 - x) \), start by distributing on the right: \( 2x - 16 = 2x - x^2 \). Next, move all terms to one side: \( x^2 - 16 = 0 \). This can be factored as \( (x - 4)(x + 4) = 0 \), giving you \( x = 4 \) and \( x = -4 \) as solutions! Don’t forget to check if your solutions are valid by substituting them back into the original equation. It’s fun to see if both values hold true! For instance, substituting \( x = 4 \) simplifies both sides to 8, confirming it’s a valid solution.
