document.write( "Question 707084: The square of a certain number is 22 less than 13 times the original. Find the answer? \n" ); document.write( "

Algebra.Com's Answer #435551 by jsmallt9(3758) $\"\"$ $\"About$

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Using \"x\" to represent the original number, \"The square of a certain number is 22 less than 13 times the original\" translates into:
\n" ); document.write( " $\"x%5E2+=+13x+-+22\"$
\n" ); document.write( "(Note how in English the \"22 less\" was first but when we translate it into a mathematical expression it goes at the end. This is usually how it works. If this seems confusing just think of this: If someone asked to figure out 22 less than 45, what would you do? 22-45 or 45-22?

\n" ); document.write( "To solve our equation we first want one side to be zero. Subtracting 13x from each side and adding 22 to each side we get:
\n" ); document.write( " $\"x%5E2+-+13x+%2B+22+=+0\"$
\n" ); document.write( "Now we factor (or use the Quadratic Formula). This factors fairly easily:
\n" ); document.write( " $\"%28x-2%29%28x-11%29+=+0\"$
\n" ); document.write( "Now we use the Zero Product Property which tells us that a product that equals zero, like ours, can only happen if one of the factors is zero. So:
\n" ); document.write( "x-2 = 0 or x-11 = 0
\n" ); document.write( "Solving these we get:
\n" ); document.write( "x = 2 or x = 11

\n" ); document.write( "So there are two possible answers to the problem. You can check if you like:
\n" ); document.write( " $\"%282%29%5E2+=+13%282%29+-+22\"$
\n" ); document.write( " $\"%2811%29%5E2+=+13%2811%29+-+22\"$
\n" ); document.write( "Both of these check out. \n" ); document.write( "

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