document.write( "Question 589117: HOW DO YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE \n" ); document.write( "

Algebra.Com's Answer #374733 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll pick a random quadratic:
\n" ); document.write( " $\"+2x%5E2+-+9x+%2B+24+\"$
\n" ); document.write( "Set equal to zero to find roots
\n" ); document.write( " $\"+2x%5E2+-+9x+%2B+24+=+0+\"$
\n" ); document.write( "Get the constant term on the right side
\n" ); document.write( "by subtracting $\"+24+\"$ from both sides
\n" ); document.write( " $\"+2x%5E2+-+9x+=+-24+\"$
\n" ); document.write( "Divide both sides by $\"+2+\"$
\n" ); document.write( " $\"+x%5E2+-+%289%2F2%29%2Ax+=+-12+\"$
\n" ); document.write( "Now take 1/2 of the coefficient of $\"x\"$ ,
\n" ); document.write( "divide it by $\"2\"$ , square it, and add it
\n" ); document.write( "to both sides
\n" ); document.write( " $\"+x%5E2+-+%289%2F2%29%2Ax+%2B+%289%2F4%29%5E2+=+-12+%2B+%289%2F4%29%5E2+\"$
\n" ); document.write( "The left side will automatically become a perfect square
\n" ); document.write( " $\"+%28+x+-+9%2F4+%29%5E2+=+-%28192%2F16%29+%2B+81%2F16+\"$
\n" ); document.write( " $\"+%28+x+-+9%2F4+%29%5E2+=+-%28+111%2F16+%29+\"$
\n" ); document.write( "Now take the square root of both sides
\n" ); document.write( " $\"+x+-+9%2F4+=+sqrt%28+1%2F16+%29%2Asqrt%28+-111%29+\"$
\n" ); document.write( " $\"+x-+9%2F4+=+%281%2F4%29%2A10.536i+\"$
\n" ); document.write( " $\"+x+=+%281%2F4%29%2A%28+9+%2B+10.536i+%29+\"$
\n" ); document.write( "and also, using the (-) square root,
\n" ); document.write( " $\"+x+=+%281%2F4%29%2A%28+9+-+10.536i+%29+\"$ \n" ); document.write( "

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