document.write( "Question 177007: Solve √(3x+1)= 7- √(x-4). Thanks for your help.
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Algebra.Com's Answer #132079 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
√(3x+1)= 7- √(x-4
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\n" ); document.write( "Square both sides to get:
\n" ); document.write( "3x+1 = 49 -14sqrt(x-4) + (x-4)
\n" ); document.write( "2x + 5 - 49 = -14sqrt(x-4)
\n" ); document.write( "2x-44 = -14sqrt(x-4)
\n" ); document.write( "x - 22 = -7sqrt(x-4)
\n" ); document.write( "Square both sides to get:
\n" ); document.write( "x^2 - 44x + 484 = 49(x-4)
\n" ); document.write( "x^2 - 44x + 484 = 49x - 196
\n" ); document.write( "x^2 - 93x + 680 = 0
\n" ); document.write( "(x-8)(x-85) = 0
\n" ); document.write( "x = 8 or x = 85
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\n" ); document.write( "Checking:√(3x+1)= 7- √(x-4
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\n" ); document.write( "Does x = 8 ?
\n" ); document.write( "sqrt(25) = 7 - sqrt(4)
\n" ); document.write( "5 = 7-2
\n" ); document.write( "Correct
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\n" ); document.write( "Does x = 85
\n" ); document.write( "sqrt(256) = 7 - sqrt(81)
\n" ); document.write( "16 = 7 - 9
\n" ); document.write( "16 = -2
\n" ); document.write( "False
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\n" ); document.write( "Only solution:
\n" ); document.write( "x = 8
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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