Quadratic Equations
1. Solve by factoring: \(\displaystyle{ 3x^4 - 27x^2 = 0} \)
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2. Solve \(\displaystyle{ \frac{x}{2x + 1} = \frac{3x + 2}{4x
+ 3}} \)
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3. Solve \(\displaystyle{ \frac{6x - 7}{x} - \frac{8}{x^2} = 5 }\)
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4. Solve \(\displaystyle{ \frac{3}{x + 3} + \frac{x}{x - 3} =
\frac{6x}{x^2 - 9} }\)
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5. Solve \(\displaystyle{ \frac{x}{x - 3} - \frac{1}{x + 2} =
\frac{9}{x^2 - x -6} }\)
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6. Solve each equation. Check your answer.
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(a) \(\displaystyle{ \sqrt[3]{3x + 1} = 4} \)
(b) \(\displaystyle{ \sqrt{2x - 3} = -1} \)
7. Solve \(\displaystyle{ \sqrt{6x + 4} = x - 2} \)
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8. Solve \(\displaystyle{ \sqrt{3y + 5} + 1 = y} \)
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9. Solve \(\displaystyle{ \sqrt{2x - 5} - \sqrt{ x - 3} =
1} \)
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10. Solve \(\displaystyle{ x^4 - 13x^2 + 36 = 0} \)
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11. Solve \(\displaystyle{4p^4 - 3p^2 -1 = 0} \)
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12. Solve \(\displaystyle{ x^{2/5} + x^{1/5} - 2 = 0}
\)
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13. Solve \(\displaystyle{ 2 x^{1/2} -5 x^{1/4} - 3 = 0} \)
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14. Solve \(\displaystyle{ x^{-2} + x^{-1} - 42 = 0} \)
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15. Solve \(\displaystyle{ (3x+1)^2 - 7(3x+1) + 6 = 0} \) solution