document.write( "Question 930177: A number increased by its square is equal to 9 times the next number. Find the number \n" ); document.write( "
Algebra.Com's Answer #565343 by ptfile(81)\"\" \"About 
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Let x = smaller number
\n" ); document.write( " x+1= larger number\r
\n" ); document.write( "\n" ); document.write( "A number increased by its square is equal to 9 times the next number
\n" ); document.write( "x^2 = 9(x+1)
\n" ); document.write( "x^2 = 9x+9\r
\n" ); document.write( "\n" ); document.write( "x^2-9x-9 = 0\r
\n" ); document.write( "\n" ); document.write( "Use Quadratic formula to solve for x
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%289+%2B-+sqrt%28+81%2B36+%29%29%2F%282%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%289+%2B-+sqrt%28+117+%29%29%2F%282%29+\"\r
\n" ); document.write( "\n" ); document.write( "x=9.9083269131959839396788319012057 or 10
\n" ); document.write( "or
\n" ); document.write( "x=-0.908326913195983939678831901205 or -1\r
\n" ); document.write( "\n" ); document.write( "Substitute x with 10
\n" ); document.write( "(10)^2 = 9(10+1)
\n" ); document.write( " 100 = 9(11)
\n" ); document.write( " 100 = 99
\n" ); document.write( "Substitute x with -1
\n" ); document.write( "(-1)^2 = 9(-1+1)
\n" ); document.write( " 1 = 9(0)
\n" ); document.write( " 1 = 0\r
\n" ); document.write( "\n" ); document.write( "The number is -1 or 10.\r
\n" ); document.write( "\n" ); document.write( "You could also use completing the square to solve for x
\n" ); document.write( "x^2-9x-9= 0
\n" ); document.write( "Add 9 on both side
\n" ); document.write( "x^2-9x+9= 0+9
\n" ); document.write( "x^2-9x = 9
\n" ); document.write( "Divide B coefficient by 2 and square it. Then add it on both side
\n" ); document.write( "x^2-9x+81/4=9+81/4
\n" ); document.write( "x^2-9x+81/4=36/4+81/4
\n" ); document.write( "x^2-9x+81/4=117/4
\n" ); document.write( " (x-9/2)^2=117/4
\n" ); document.write( "Square root on both side
\n" ); document.write( "√(x-9/2)^2 = √117/4
\n" ); document.write( "x-9/2 = 3/2√13
\n" ); document.write( "Add 9/2 on both side. Add ± on the right side.
\n" ); document.write( "x-9/2+9/2 =9/2±3/2√13
\n" ); document.write( "x = 9/2 ±3/2√13
\n" ); document.write( "
\n" ); document.write( "x = 9.9083269131959839396788319012057 or 10
\n" ); document.write( "or
\n" ); document.write( "x = -0.908326913195983939678831901205 or -1\r
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