To solve the quadratic equation \( x^2 + 54x = -729 \) using the perfect square trinomial pattern, follow these steps:
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Move all terms to one side of the equation: \[ x^2 + 54x + 729 = 0 \]
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Rewrite the left side as a perfect square trinomial. To do this, we need to complete the square for \( x^2 + 54x \):
- Take half of the coefficient of \( x \) (which is 54), square it, and add it to both sides of the equation: \[ \left(\frac{54}{2}\right)^2 = 27^2 = 729 \]
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Now, rewrite the equation: \[ (x + 27)^2 = 0 \]
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Take the square root of both sides: \[ x + 27 = 0 \]
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Solve for \( x \): \[ x = -27 \]
Thus, the solution to the equation \( x^2 + 54x = -729 \) is: \[ x = -27 \]
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