document.write( "Question 1010950: Find two consecutive integers where the sum of the squares of the two integers equals 421. \n" ); document.write( "
Algebra.Com's Answer #626455 by addingup(3677)\"\" \"About 
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x^2+(x+1)^2= 421
\n" ); document.write( "Expand out terms of the left hand side:
\n" ); document.write( "2x^2+2x+1 = 421
\n" ); document.write( "Divide both sides by 2:
\n" ); document.write( "x^2+x+1/2 = 421/2
\n" ); document.write( "Subtract 1/2 from both sides:
\n" ); document.write( "x^2+x = 210
\n" ); document.write( "Add 1/4 to both sides:
\n" ); document.write( "x^2+x+1/4 = 841/4
\n" ); document.write( "Write the left hand side as a square:
\n" ); document.write( "(x+1/2)^2 = 841/4
\n" ); document.write( "Take the square root of both sides and, like with every quadratic, we get two possible outcomes:
\n" ); document.write( "x+1/2 = 29/2 or x+1/2 = -29/2
\n" ); document.write( "Subtract 1/2 from all sides:
\n" ); document.write( "x = 14 or x = -15
\n" ); document.write( "OK, let's try these and see which one is correct, start with 14:
\n" ); document.write( "14^2+(14+1)^2= 421
\n" ); document.write( "14^2+15^2= 421
\n" ); document.write( "196+225= 421
\n" ); document.write( "421= 421 So 14 is our number, and the problem says \"consecutive integers\", thus the other number is 15
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