document.write( "Question 165936: The perimeter of one square exceeds that of another by 16 and its area is 44 less than the 4 times the area of the other. What is the length of the side of each square?
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Algebra.Com's Answer #122288 by nerdybill(7384)\"\" \"About 
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The perimeter of one square exceeds that of another by 16 and its area is 44 less than the 4 times the area of the other. What is the length of the side of each square?
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\n" ); document.write( "Perimeter of any square equals 4 times the length of a side.
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\n" ); document.write( "Let x = length of a side of smaller square
\n" ); document.write( "and y = length of a side of larger square
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\n" ); document.write( "From:\"The perimeter of one square exceeds that of another by 16\"
\n" ); document.write( "4x = 4y+16
\n" ); document.write( "dividing through by 4:
\n" ); document.write( "x = y + 4 (equation 1)
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\n" ); document.write( "From:\"its area is 44 less than the 4 times the area of the other\"
\n" ); document.write( "x^2 = 4y^2 - 44 (equation 2)
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\n" ); document.write( "Substitute the value of 'x' from equation 1 into equation 2 and solve for y:
\n" ); document.write( "x^2 = 4y^2 - 44
\n" ); document.write( "(y + 4)^2 = 4y^2 - 44
\n" ); document.write( "y^2 + 8y + 16 = 4y^2 - 44
\n" ); document.write( "8y + 16 = 3y^2 - 44
\n" ); document.write( "16 = 3y^2 - 8y - 44
\n" ); document.write( "0 = 3y^2 - 8y - 60
\n" ); document.write( "Solving using the quadratic equation will yield:
\n" ); document.write( "x = {6, -3.33333333333333}
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\n" ); document.write( "We can toss out the negative answer leaving:
\n" ); document.write( "x = 6
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\n" ); document.write( "To find y, substitute x into equation 1 and solve:
\n" ); document.write( "x = y + 4
\n" ); document.write( "6 = y + 4
\n" ); document.write( "2 = y
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\n" ); document.write( "Solution: 6 and 2
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\n" ); document.write( "Below is the details of the quadratic solution:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"3x%5E2%2B-8x%2B-60+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-8%29%5E2-4%2A3%2A-60=784\".
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\n" ); document.write( " Discriminant d=784 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--8%2B-sqrt%28+784+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+784+%29%29%2F2%5C3+=+6\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-8%29-sqrt%28+784+%29%29%2F2%5C3+=+-3.33333333333333\"
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\n" ); document.write( " Quadratic expression \"3x%5E2%2B-8x%2B-60\" can be factored:
\n" ); document.write( " \"3x%5E2%2B-8x%2B-60+=+3%28x-6%29%2A%28x--3.33333333333333%29\"
\n" ); document.write( " Again, the answer is: 6, -3.33333333333333.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-8%2Ax%2B-60+%29\"

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