document.write( "Question 862390: sum of the squares of two numbers is 100. sum of the numbers is 2. find the numbers. \n" ); document.write( "

Algebra.Com's Answer #519642 by ben720(159) $\"\"$ $\"About$

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Let first number = x
\n" ); document.write( "Let second = 2-x, as they add to two\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B%282-x%29%5E2=100\"$
\n" ); document.write( "Square 2-x
\n" ); document.write( " $\"x%5E2%2Bx%5E2-4x%2B4=100\"$
\n" ); document.write( "Combine like terms
\n" ); document.write( " $\"2x%5E2-4x%2B4=100\"$
\n" ); document.write( "Divide both sides by 2
\n" ); document.write( " $\"x%5E2-2x%2B2=50\"$
\n" ); document.write( "Subtract 50 from both sides
\n" ); document.write( " $\"x%5E2-2x-48=0\"$
\n" ); document.write( "Use the quadratic formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28+-2%5E2-4%2A1%2A-48+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%284%2B192%29%29%2F2+\"$
\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28196%29%29%2F2\"$
\n" ); document.write( " $\"x=%282%2B14%29%2F2\"$ OR $\"x=%282-14%29%2F2\"$
\n" ); document.write( " $\"x=8\"$ OR $\"x=-6\"$
\n" ); document.write( "

The numbers are 8 and -6

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