To solve the quadratic equation \(\frac{1}{4}x^2 + 2x + 4 = 0\) using the perfect square trinomial pattern, we first want to rewrite this equation in a more manageable form.
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Multiply through by 4 to eliminate the fraction: \[ x^2 + 8x + 16 = 0. \]
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Rearrange the equation: \[ x^2 + 8x + 16 = 0. \]
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Now, notice that \(x^2 + 8x + 16\) can be factored as a perfect square: \[ (x + 4)^2 = 0. \]
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Solve for \(x\): \[ x + 4 = 0 \implies x = -4. \]
Thus, the solution to the equation \(\frac{1}{4}x^2 + 2x + 4 = 0\) is: \[ \boxed{-4}. \]
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