document.write( "Question 179467: Can you please help solve for the following:
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Algebra.Com's Answer #134403 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "A radical term is already isolated on the left, so square both sides:\r\n" );
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document.write( "Take away the radical and exponent on the left, write the square on\r\n" );
document.write( "the right as the product of the base times itself:\r\n" );
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document.write( "Use \"FOIL\" on the right:\r\n" );
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document.write( "Combine like terms on the right, take away radical and exponent\r\n" );
document.write( "in the last term on the right:\r\n" );
document.write( "\"matrix%281%2C3%2C14-x%2C+%22=%22%2C+36-12sqrt%28x%2B4%29%2Bx%2B4+++%29\"\r\n" );
document.write( "Isolate the radical term on the left side:\r\n" );
document.write( "\"matrix%281%2C3%2C12sqrt%28x%2B4%29%2C%22=%22%2C36%2Bx%2B4-14%2Bx+%29\"\r\n" );
document.write( "Combine like terms:\r\n" );
document.write( "\"matrix%281%2C3%2C12sqrt%28x%2B4%29%2C%22=%22%2C26%2B2x+%29\"\r\n" );
document.write( "Notice that every term can be divided by 2, so do so:\r\n" );
document.write( "\"matrix%281%2C3%2C6sqrt%28x%2B4%29%2C%22=%22%2C13%2Bx+%29\"\r\n" );
document.write( "Square both sides:\r\n" );
document.write( "\"matrix%281%2C3%2C%286sqrt%28x%2B4%29%29%5E2%2C%22=%22%2C%2813%2Bx%29%5E2+%29\"\r\n" );
document.write( "\"matrix%281%2C3%2C6%5E2%28sqrt%28x%2B4%29%5E2%29%2C%22=%22%2C%2813%2Bx%29%2813%2Bx%29+%29\"\r\n" );
document.write( "\"matrix%281%2C3%2C36%28x%2B4%29%2C%22=%22%2C13%5E2%2B13x%2B13x%2Bx%5E2+%29\"\r\n" );
document.write( "\"matrix%281%2C3%2C36x%2B144%2C%22=%22%2C169%2B26x%2Bx%5E2%29\"\r\n" );
document.write( "Get 0 on the left:\r\n" );
document.write( "\"matrix%281%2C3%2C0%2C%22=%22%2C169%2B26x%2Bx%5E2-36x-144%29\"\r\n" );
document.write( "\"matrix%281%2C3%2C0%2C%22=%22%2C25-10x%2Bx%5E2%29\"\r\n" );
document.write( "Rearrange right side in descending order:\r\n" );
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document.write( "Switch right side and left side:\r\n" );
document.write( "\"matrix%281%2C3%2Cx%5E2-10x%2B25%2C%22=%22%2C0%29\"\r\n" );
document.write( "Factor left side:\r\n" );
document.write( "\"matrix%281%2C3%2C%28x-5%29%28x-5%29%2C%22=%22%2C0%29\"\r\n" );
document.write( "Use zero-factor principle:\r\n" );
document.write( "\"matrix%282%2C3%2C%0D%0Ax-5=0%2C%22++++++%22%2Cx-5=0%2C%0D%0A++x=5%2C%22++++++%22%2Cx=5%29\"   \r\n" );
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document.write( "We get one solution \"x=5\"\r\n" );
document.write( "However this might be an extraneous\r\n" );
document.write( "(bogus) solution, for sometimes you\r\n" );
document.write( "get those when you square both sides\r\n" );
document.write( "of an equation.  So we must check\r\n" );
document.write( "it to see if it satisfies the original\r\n" );
document.write( "radical equation:\r\n" );
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document.write( "\"matrix%281%2C3%2Csqrt%2814+-+5%29%2C+%22=%22%2C+6+-+sqrt%285+%2B+4%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2Csqrt%289%29%2C+%22=%22%2C+6+-+sqrt%289%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2C3%2C+%22=%22%2C+6+-+3%29\"\r\n" );
document.write( "\"matrix%281%2C3%2C3%2C+%22=%22%2C+3%29\" \r\n" );
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document.write( "It does, so \"x=5\" is the only solution.\r\n" );
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document.write( "Edwin
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