document.write( "Question 83494: I have a problem that state: Solve by completing the square: 6x=3X^2-2. I know that I need factor out the sides but what then? \n" ); document.write( "

Algebra.Com's Answer #60020 by Earlsdon(6294) $\"\"$ $\"About$

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Start by putting your equation into the \"standard form\" for quadratic equations: $\"ax%5E2%2Bbx%2Bc+=+0\"$
\n" ); document.write( " $\"6x+=+3x%5E2-2\"$ Subtract 6x from both sides.
\n" ); document.write( " $\"3x%5E2-6x-2+=+0\"$ Now you need to make the coefficient of the $\"x%5E2\"$ term equal to 1. You do this here by dividing through by 3.
\n" ); document.write( " $\"3x%5E2%2F3-6x%2F3-2%2F3+=+0%2F3\"$ Simplify this.
\n" ); document.write( " $\"x%5E2-2x-2%2F3+=+0\"$ Next, you'll add $\"2%2F3\"$ to both sides.
\n" ); document.write( " $\"x%5E2-2x+=+2%2F3\"$ Now you'll complete the square by adding the square of half the x-coefficient $\"%28-2%2F2%29%5E2+=+1\"$ to both sides.
\n" ); document.write( " $\"x%5E2-2x%2B1+=+%282%2F3%29%2B1\"$ Simplify this.
\n" ); document.write( " $\"x%5E2-2x%2B1+=+5%2F3\"$ Now factor the left side.
\n" ); document.write( " $\"%28x-1%29%28x-1%29+=+5%2F3\"$ Simplify this.
\n" ); document.write( " $\"%28x-1%29%5E2+=+5%2F3\"$ Notice that you now have a \"square\" on the left side. Take the square root of both sides.
\n" ); document.write( " $\"x-1+=+sqrt%285%2F3%29\"$ or $\"x-1+=+-sqrt%285%2F3%29\"$ Add 1 to both sides of each equation.
\n" ); document.write( " $\"x+=+1%2Bsqrt%285%2F3%29\"$ or $\"x+=+1-sqrt%285%2F3%29\"$ These are the two solutions. \n" ); document.write( "

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