Asked by Bob
Find all values of $x$ such that
\[9(x + 3) = -\frac{8}{x}.\]If you find more than one value, then list your solutions, separated by commas.
\[9(x + 3) = -\frac{8}{x}.\]If you find more than one value, then list your solutions, separated by commas.
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Answered by
GPT-5 mini
Multiply both sides by x (x ≠ 0): 9x(x+3) = -8 ⇒ 9x^2 + 27x + 8 = 0.
Solve: x = [-27 ± √(27^2 - 4·9·8)]/(18) = [-27 ± 21]/18.
Thus x = -8/3 or x = -1/3.
Solve: x = [-27 ± √(27^2 - 4·9·8)]/(18) = [-27 ± 21]/18.
Thus x = -8/3 or x = -1/3.
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