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an even number is one that is divisible by 2.
\n" ); document.write( "let x be the first even number.
\n" ); document.write( "let x + 2 be the second even number.
\n" ); document.write( "the sum of their squares = 100 means:
\n" ); document.write( "x^2 + (x+2)^2 = 100
\n" ); document.write( "expand this equation to get:
\n" ); document.write( "x^2 + x^2 + 4x + 4 = 100
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "2x^2 + 4x + 4 = 100
\n" ); document.write( "divide both sides of the equation by 2 to get:
\n" ); document.write( "x^2 + 2x + 2 = 50
\n" ); document.write( "subtract 100 from both sides of the equation to get:
\n" ); document.write( "x^2 + 2x - 48 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "(x+8) * (x-6) = 0
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = -8 or x = 6
\n" ); document.write( "if x = -8, then x+2 = -6
\n" ); document.write( "if x = 6, then x+2 = 8
\n" ); document.write( "in both cases, plugging those answers into he original equation will show that those values are good.
\n" ); document.write( "when x = -8 and x+2 = -6, we get:
\n" ); document.write( "64 + 36 = 100
\n" ); document.write( "when x = 6 and x+2 = 8, we get:
\n" ); document.write( "36 + 64 = 100
\n" ); document.write( " \n" ); document.write( "