document.write( "Question 188824: Solve the quadratic equation by completing the square.\r
\n" ); document.write( "\n" ); document.write( " $\"+2x%5E2+\"$ + 5x - 8 = 0 \r
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\n" ); document.write( "\n" ); document.write( "Could you please provide me a detailed explanation of how to obtain the answer \n" ); document.write( "

Algebra.Com's Answer #141613 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Solve the quadratic equation by completing the square.
\n" ); document.write( "2x^2 + 5x - 8 = 0
\n" ); document.write( ":
\n" ); document.write( "We need to have the coefficient of x^2 equal 1, divide equation by 2
\n" ); document.write( "x^2 + $\"5%2F2\"$ x - 4 = 0
\n" ); document.write( ":
\n" ); document.write( "x^2 + $\"5%2F2\"$ x + ___ = 4
\n" ); document.write( "Choose a value that will complete the square
\n" ); document.write( "Take half the coefficient of x and square it to accomplish this:
\n" ); document.write( " $\"%281%2F2%29%2A%285%2F2%29+=+%285%2F4%29\"$ Square this and you have $\"25%2F16\"$ , add to both sides
\n" ); document.write( "x^2 + $\"5%2F2\"$ x + $\"25%2F16\"$ = 4 + $\"25%2F16\"$
\n" ); document.write( "x^2 + $\"5%2F2\"$ x + $\"25%2F16\"$ = $\"64%2F16\"$ + $\"25%2F16\"$
\n" ); document.write( "x^2 + $\"5%2F2\"$ x + $\"25%2F16\"$ = $\"89%2F16\"$
\n" ); document.write( "which is
\n" ); document.write( "(x + $\"5%2F4\"$ )^2 = $\"89%2F16\"$
\n" ); document.write( "Find the square root of both sides:
\n" ); document.write( "x + $\"5%2F4\"$ = +/- $\"sqrt%2889%2F16%29\"$
\n" ); document.write( ":
\n" ); document.write( "x = $\"-5%2F4\"$ +/- $\"sqrt%2889%2F16%29\"$
\n" ); document.write( "Extract the perfect square
\n" ); document.write( "x = $\"-5%2F4\"$ +/- $\"%281%2F4%29sqrt%2889%29\"$
\n" ); document.write( ":
\n" ); document.write( "x = $\"%28-5+%2B+sqrt%2889%29%29%2F4\"$
\n" ); document.write( "and
\n" ); document.write( "x = $\"%28-5+-+sqrt%2889%29%29%2F4\"$ \n" ); document.write( "

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