document.write( "Question 1061504: Solve the following equation by first doing a substitution to make it a quadratic. \r
\n" ); document.write( "\n" ); document.write( "3x^-2 + x^-1 -24=0 \n" ); document.write( "
Algebra.Com's Answer #676287 by MathTherapy(10552)\"\" \"About 
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\n" ); document.write( "Solve the following equation by first doing a substitution to make it a quadratic. \r
\n" ); document.write( "\n" ); document.write( "3x^-2 + x^-1 -24=0
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\"3x%5E%28-+2%29+%2B+x%5E%28-+1%29+-+24+=+0\"
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document.write( "The SIMPLE substitution: Let \"matrix%281%2C3%2C+a%2C+be%2C+x%5E%28-+1%29%29\"
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document.write( "Then \"matrix%281%2C3%2C+3x%5E%28-+2%29%2C+becomes%2C+3a%5E2%29\", and \"3x%5E%28-+2%29+%2B+x%5E%28-+1%29+-+24+=+0\" becomes: \"3a%5E2+%2B+a+-+24+=+0\"
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document.write( "\"3a%5E2+%2B+9a+-+8a+-+24+=+0\" ------ Repalacing a, with 9a - 8a
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document.write( "3a(a + 3) - 8(a + 3) = 0
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document.write( "(a + 3)(3a - 8) = 0
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document.write( "\"matrix%281%2C7%2C+a%2C+%22=%22%2C+-+3%2C+or%2C+a%2C+%22=%22%2C+8%2F3%29\" \r
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document.write( "\"x%5E%28-+1%29+=+-+3\" ------- Substituting back \"matrix%281%2C5%2C+a%2C+or%2C+-+3%2C+for%2C+x%5E%28-+1%29%29\"
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document.write( "\"x%5E%28%28-+1%29+%2A+%28-+1%29%29+=+%28-+3%29%5E%28-+1%29\" ------ Raising each side to the - 1 power
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document.write( "\"highlight_green%28x+=+-+1%2F3%29\" 
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document.write( "Substitute this value for x (\"-+1%2F3\") into the original equation. If this value satisfies the original equation, then \"x+=+-+1%2F3\" is a solution to the equation. 
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document.write( "This value for x DOES SATISFY the equation.\r
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document.write( "\"x%5E%28-+1%29+=+%28-+8%29%2F3\" ------- Substituting back \"matrix%281%2C5%2C+a%2C+or%2C+8%2F3%2C+for%2C+x%5E%28-+1%29%29\"
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document.write( "\"x%5E%28%28-+1%29+%2A+%28-+1%29%29+=+%288%2F3%29%5E%28-+1%29\" ------ Raising each side to the - 1 power
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document.write( "\"highlight_green%28x+=+3%2F8%29\" 
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document.write( "Substitute this value for x (\"3%2F8\") into the original equation. If this value satisfies the original equation, then \"x+=+3%2F8\" is a solution to the equation.
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document.write( "This value for x DOES SATISFY the equation. \n" );
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