To complete the square for the equation \( x^2 + 6x = 90 \), we start by rearranging it:
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Move the constant to the right side: \[ x^2 + 6x - 90 = 0 \] or, \[ x^2 + 6x = 90 \]
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To complete the square, we take the coefficient of \( x \), which is 6, divide it by 2 to get 3, and then square it to get 9.
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Add and subtract this square (9) inside the equation: \[ x^2 + 6x + 9 - 9 = 90 \] \[ (x + 3)^2 - 9 = 90 \]
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Now add 9 to both sides: \[ (x + 3)^2 = 90 + 9 \] \[ (x + 3)^2 = 99 \]
Thus, the equivalent equation after completing the square is: \[ (x + 3)^2 = 99 \]
So, the correct answer is (x + 3)^2 = 99.