SOLUTION: Solve the following equation by first doing a substitution to make it a quadratic. 3x^-2 + x^-1 -24=0

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Question 1061504: Solve the following equation by first doing a substitution to make it a quadratic.
3x^-2 + x^-1 -24=0

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!

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Try to factorize.




OR







Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Solve the following equation by first doing a substitution to make it a quadratic.
3x^-2 + x^-1 -24=0

The SIMPLE substitution: Let
Then , and becomes:
------ Repalacing a, with 9a - 8a
3a(a + 3) - 8(a + 3) = 0
(a + 3)(3a - 8) = 0

------- Substituting back
------ Raising each side to the - 1 power

Substitute this value for x () into the original equation. If this value satisfies the original equation, then is a solution to the equation.
This value for x DOES SATISFY the equation.
------- Substituting back
------ Raising each side to the - 1 power

Substitute this value for x () into the original equation. If this value satisfies the original equation, then is a solution to the equation.
This value for x DOES SATISFY the equation.
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