document.write( "Question 1872: Two consecutive integers are added. The square of their sum is 361. What are the integers? \n" ); document.write( "

Algebra.Com's Answer #712 by Ne0(6) $\"\"$ $\"About$

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The first step in solving problems like this is that you need to define the unknowns that is define what it is your solving for.
\n" ); document.write( "We start by letting the first integer be x.
\n" ); document.write( "Since the integers are consecutive that means they come one after the other so you can let the second integer be x+1.
\n" ); document.write( "The square of their sum is simply adding the two terms together then squaring them like so: $\"%28x%2Bx%2B1%29%5E2\"$ . Adding the like terms give us: $\"%282x%2B1%29%5E2\"$ .
\n" ); document.write( "It says the square of their sums is equal to 361 so you now have $\"%282x%2B1%29%5E2=361\"$ .
\n" ); document.write( "The next step is to solve for x. We can accomplish this by first taking the square roots of both sides like so: $\"sqrt%28%282x%2B1%29%5E2%29=sqrt%28361%29\"$ . After taking the square root we should arrive with $\"19%2B-0=%282x%2B1%29\"$ . I had to stick the zero in because the equation editor would not agree with me otherwise. We get x by itself by subtracting 1 then dividing both sides by 2 to get $\"x=%28-1%2B-19%29%2F%282%29\"$ .
\n" ); document.write( "Simplifying we get x=9 and x=-10.
\n" ); document.write( "By back substituting our value of x into x+1 we get x+1=10 and x+1=-9.
\n" ); document.write( "We now have all the integers which are 9,-10,10,-9.
\n" ); document.write( "I hope this helps you in solving for problems of this type. \n" ); document.write( "

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