Absolutely! Here's the solution for the equation 9s² - 4 = -6s:
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Rearrange to Standard Form: Add 6s to both sides: 9s² + 6s - 4 = 0
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Use the Quadratic Formula:
- a = 9, b = 6, c = -4
- s = (-b ± √(b² - 4ac)) / 2a
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Substitute and Simplify: s = (-6 ± √(6² - 4 * 9 * -4)) / (2 * 9) s = (-6 ± √(180)) / 18 s = (-6 ± 6√5) / 18
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Simplify the Solutions: s₁ = (-1 + √5) / 3 s₂ = (-1 - √5) / 3
Therefore, the solutions to the equation are:
- s₁ = (-1 + √5) / 3
- s₂ = (-1 - √5) / 3
