document.write( "Question 274322: The roots of the equation 2x squared-10x+8=0 represent the dimension of the rectangle. what is the area of the rectangle \n" ); document.write( "
Algebra.Com's Answer #200221 by jim_thompson5910(35256)\"\" \"About 
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For more help, check out this quadratic formula solver.\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"2%2Ax%5E2-10%2Ax%2B8=0\" ( notice \"a=2\", \"b=-10\", and \"c=8\")
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\n" ); document.write( " \"x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A2%2A8+%29%29%2F%282%2A2%29\" Plug in a=2, b=-10, and c=8
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\n" ); document.write( " \"x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A2%2A8+%29%29%2F%282%2A2%29\" Negate -10 to get 10
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\n" ); document.write( " \"x+=+%2810+%2B-+sqrt%28+100-4%2A2%2A8+%29%29%2F%282%2A2%29\" Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because \"%28-10%29%5E2=-10%2A-10=100\".)
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\n" ); document.write( " \"x+=+%2810+%2B-+sqrt%28+100%2B-64+%29%29%2F%282%2A2%29\" Multiply \"-4%2A8%2A2\" to get \"-64\"
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\n" ); document.write( " \"x+=+%2810+%2B-+sqrt%28+36+%29%29%2F%282%2A2%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%2810+%2B-+6%29%2F%282%2A2%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%2810+%2B-+6%29%2F4\" Multiply 2 and 2 to get 4
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%2810+%2B+6%29%2F4\" or \"x+=+%2810+-+6%29%2F4\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%2810+%2B+6%29%2F4\"
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\n" ); document.write( " \"x=16%2F4\" Add the terms in the numerator
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\n" ); document.write( " \"x=4\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=4\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%2810+-+6%29%2F4\"
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\n" ); document.write( " \"x=4%2F4\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=1\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=1\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=4\" or \"x=1\"
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\n" ); document.write( "\n" ); document.write( "Since the roots are \"x=1\" or \"x=4\", this means that the length is 4 units and the width is 1 unit. So the area is simply A=4*1=4 square units. \n" ); document.write( "
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