document.write( "Question 437377: Can you please solve the equation by completing the square: -10x=3x²-2 \n" ); document.write( "

Algebra.Com's Answer #302616 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Can you please solve the equation by completing the square: -10x = 3x² - 2
\n" ); document.write( ":
\n" ); document.write( "Re-write the equation in the form
\n" ); document.write( "3x^2 + 10x + ___ = 2
\n" ); document.write( "The coefficient of x^2 has to be 1, divide by 3, results:
\n" ); document.write( "x^2 + $\"10%2F3\"$ x + ____ = $\"2%2F3\"$
\n" ); document.write( ":
\n" ); document.write( "Find the term which completes the square; (10/6)^2 = (100/36) reduces to $\"25%2F9\"$
\n" ); document.write( "x^2 + $\"10%2F3\"$ x + $\"25%2F9\"$ = $\"2%2F3\"$ + $\"25%2F9\"$
\n" ); document.write( ":
\n" ); document.write( "x^2 + $\"10%2F3\"$ x + $\"25%2F9\"$ = $\"6%2F9\"$ + $\"25%2F9\"$
\n" ); document.write( ":
\n" ); document.write( "x^2 + $\"10%2F3\"$ x + $\"25%2F9\"$ = $\"31%2F9\"$
\n" ); document.write( ":
\n" ); document.write( "(x + $\"5%2F3\"$ )^2 = $\"31%2F9\"$
\n" ); document.write( ":
\n" ); document.write( "x + $\"5%2F3\"$ = +/- $\"sqrt%2831%2F9%29\"$
\n" ); document.write( ":
\n" ); document.write( "Two solutions
\n" ); document.write( "x = $\"-5%2F3\"$ + $\"1%2F3\"$ $\"sqrt%2831%29\"$
\n" ); document.write( "We can write it:
\n" ); document.write( "x = $\"%28-5+%2B+sqrt%2831%29%29%2F3\"$
\n" ); document.write( "and
\n" ); document.write( "x = $\"%28-5+-+sqrt%2831%29%29%2F3\"$ \n" ); document.write( "

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