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You can put this solution on YOUR website!
x is the value of one of the numbers.
\n" ); document.write( "y is the value of the other number.\r
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\n" ); document.write( "\n" ); document.write( "x = y + 5 is one of your equations.
\n" ); document.write( "x^2 + y^2 = 193 is the other of your equations.\r
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\n" ); document.write( "\n" ); document.write( "in the second equation, replace x with y + 5 to get:
\n" ); document.write( "(y + 5)^2 + y^2 = 193
\n" ); document.write( "simplify to get:
\n" ); document.write( "y^2 + 10y + 25 + y^2 = 193
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "2y^2 + 10y + 25 = 193
\n" ); document.write( "subtract 193 from both sides of the equation to get:
\n" ); document.write( "2y^2 + 10y - 168 = 0
\n" ); document.write( "divide both sides of this equation by 2 to get:
\n" ); document.write( "y^2 + 5y - 84 = 0
\n" ); document.write( "factor to get:
\n" ); document.write( "(y + 12) * (y - 7) = 0
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = -12 or y = 7\r
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\n" ); document.write( "\n" ); document.write( "value of y has to be positive, so y = 7 is a possible solution.
\n" ); document.write( "x = y + 5, therefore x = 12
\n" ); document.write( "your number appear to be 12 and 7.
\n" ); document.write( "12 - 7 = 5, which satisfies one of the requirements.
\n" ); document.write( "12^2 + 7^2 = 144 + 49 = 193, which satisfies the other requirement.\r
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\n" ); document.write( "\n" ); document.write( "your solution is that the numbers are 7 and 12.\r
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