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Solve the following quadratic equation using the perfect square trinomial pattern: x^2+54x=−729 x=?
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GPT-5 mini
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x^2 + 54x = -729
Complete the square: add 729 to both sides (since (54/2)^2 = 27^2 = 729):
x^2 + 54x + 729 = 0 → (x + 27)^2 = 0
So x + 27 = 0 and x = -27 (double root).
Check: (-27)^2 + 54(-27) = 729 - 1458 = -729.
Complete the square: add 729 to both sides (since (54/2)^2 = 27^2 = 729):
x^2 + 54x + 729 = 0 → (x + 27)^2 = 0
So x + 27 = 0 and x = -27 (double root).
Check: (-27)^2 + 54(-27) = 729 - 1458 = -729.
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