document.write( "Question 211413This question is from textbook Elementary and Intermediate Algebra, 3e
\n" ); document.write( ": I am stumped...I can not figure these two problems out for the life of me...can someone please assist me with these two problems?\r
\n" ); document.write( "\n" ); document.write( "Find all real solutions to each equation.\r
\n" ); document.write( "\n" ); document.write( "64) \"x%5E2+%2B+x+%2B+sqrt+%28x%5E2+%2B+x%29+-+2+=+0\"\r
\n" ); document.write( "\n" ); document.write( "Find all real and imaginary solutions to each equation.\r
\n" ); document.write( "\n" ); document.write( "70) \"b%5E4+%2B+13b%5E2+%2B+36+=+0\"
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Algebra.Com's Answer #159775 by Edwin McCravy(20055)\"\" \"About 
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I am stumped...I can not figure these two problems out for the life of me...can someone please assist me with these two problems?
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document.write( "\"x%5E2+%2B+x+%2B+sqrt+%28x%5E2+%2B+x%29+-+2+=+0\" \r\n" );
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document.write( "We group the first two terms as one term:\r\n" );
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document.write( "\"%28x%5E2+%2B+x%29+%2B+sqrt+%28x%5E2+%2B+x%29+-+2+=+0\"\r\n" );
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document.write( "Now there are three terms on the left.  Notice \r\n" );
document.write( "that if we square the variable of the\r\n" );
document.write( "middle term \"sqrt%28x%5E2%2Bx%29\", we get the \r\n" );
document.write( "variable of the first term \"%28x%5E2%2Bx%29\".\r\n" );
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document.write( "Therefore we substitute the letter \"\"u\"\" for\r\n" );
document.write( "the variable of the middle term, that is\r\n" );
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document.write( "\"sqrt%28x%5E2%2Bx%29=u\"\r\n" );
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document.write( "Then squaring both sides we have\r\n" );
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document.write( "\"%28x%5E2%2Bx%29=u%5E2\"\r\n" );
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document.write( "So we substitute and\r\n" );
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document.write( "\"%28x%5E2+%2B+x%29+%2B+sqrt+%28x%5E2+%2B+x%29+-+2+=+0\"\r\n" );
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document.write( "becomes simply\r\n" );
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document.write( "\"u%5E2%2Bu-2=0\"\r\n" );
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document.write( "Which we factor \r\n" );
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document.write( "\"%28u%2B2%29%28u-1%29=0\"\r\n" );
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document.write( "and solve getting \"u=-2\" and \"u=1\"\r\n" );
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document.write( "Since \"sqrt%28x%5E2%2Bx%29=u\" and a square root\r\n" );
document.write( "can never be negative in real numbers, we can \r\n" );
document.write( "rule out \"u=-2\". So \"u=1\"\r\n" );
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document.write( "Substituting back\r\n" );
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document.write( "\"%28x%5E2%2Bx%29=u%5E2\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"%28x%5E2%2Bx%29=1%5E2\"\r\n" );
document.write( "\"x%5E2%2Bx=1\"\r\n" );
document.write( "\"x%5E2%2Bx-1=0\"\r\n" );
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document.write( "We use the quadratic formula:\r\n" );
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document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" \r\n" );
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document.write( " \"x+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%2A%281%29%2A%28-1%29+%29%29%2F%282%2A%281%29%29+\"\r\n" );
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document.write( " \"x+=+%28-1+%2B-+sqrt%28+1%2B4+%29%29%2F2+\"\r\n" );
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document.write( " \"x+=+%28-1+%2B-+sqrt%285%29%29%2F2+\"\r\n" );
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document.write( "Find all real and imaginary solutions to each equation. \r\n" );
document.write( "70) \"b%5E4+%2B+13b%5E2+%2B+36+=+0\"\r\n" );
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document.write( "Notice that if we square the variable of the\r\n" );
document.write( "middle term \"sqrt%28b%5E2%29\", we get the \r\n" );
document.write( "variable of the first term \"%28b%5E4%29\".\r\n" );
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document.write( "Therefore we substitute the letter \"\"u\"\" for\r\n" );
document.write( "the variable of the middle term, that is\r\n" );
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document.write( "\"b%5E2=u\"\r\n" );
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document.write( "and squaring both sides:\r\n" );
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document.write( "\"b%5E4=u%5E2\"\r\n" );
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document.write( "So we substitute and\r\n" );
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document.write( "\"b%5E4+%2B+13b%5E2+%2B+36+=+0\"\r\n" );
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document.write( "becomes simply\r\n" );
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document.write( "\"u%5E2%2B13u%2B36=0\"\r\n" );
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document.write( "Which we factor \r\n" );
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document.write( "\"%28u%2B9%29%28u%2B4%29=0\"\r\n" );
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document.write( "and solve getting \"u=-9\" and \"u=-4\"\r\n" );
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document.write( "Now since \"b%5E2=u\", we have\r\n" );
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document.write( "\"b%5E2=-9\" and \"b%5E2=-4\"\r\n" );
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document.write( "Taking square roots:\r\n" );
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document.write( "\"b=%22+%22%2B-sqrt%28-9%29\" and \"b=%22+%22%2B-sqrt%28-4%29\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"b\"\"3i\" and \"b\"\"2i\"\r\n" );
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document.write( "Edwin
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