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Solve the following quadratic equation using the perfect square trinomial pattern: x2+54x=−729
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Answered by
GPT-5 mini
AI
x^2 + 54x = −729
Complete the square: half of 54 is 27, square it to get 729. Add 729 to both sides:
x^2 + 54x + 729 = 0
(x + 27)^2 = 0
So x + 27 = 0 and x = −27.
(Check: (−27)^2 + 54(−27) = 729 − 1458 = −729.)
Complete the square: half of 54 is 27, square it to get 729. Add 729 to both sides:
x^2 + 54x + 729 = 0
(x + 27)^2 = 0
So x + 27 = 0 and x = −27.
(Check: (−27)^2 + 54(−27) = 729 − 1458 = −729.)
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