document.write( "Question 69254: Solve by completing the square.
\n" ); document.write( " 4x^2 + 2x – 3 = 0\r
\n" ); document.write( "\n" ); document.write( "Hellllpppp, pleeeeeaaaaase!!! \n" ); document.write( "
Algebra.Com's Answer #49354 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"4x%5E2%2B2x-3=0\"Move the -3 to the right side by adding 3 to both sides
\n" ); document.write( "\"4%28x%5E2%2B%282%2F4%29x%29=3\"Factor out a 4 to get leading coefficient equal to 1
\n" ); document.write( "\"4%28x%5E2%2B%281%2F2%29%2Ax%2B__%29=3\"Complete the square by taking half of the x coefficient and squaring it \"%28%281%2F2%29%2A%281%2F2%29%29%5E2=1%2F16\"
\n" ); document.write( "\"4%28x%5E2%2B%281%2F2%29%2Ax%2B1%2F16%29=3%2B4%2F16\"add that value to both sides (remember the 4 was factored out, so the complete value should be 4/16 or 1/4)
\n" ); document.write( "\"4%28x%5E2%2B%281%2F2%29%2Ax%2B1%2F16%29=3%2B1%2F4\"The left side of the equation then becomes 4(x+1/4)^2 (because if it's foiled it becomes \"4%28x%5E2%2B%281%2F2%29%2Ax%2B1%2F16%29\" again).
\n" ); document.write( "\"4%28x%2B1%2F4%29%5E2=12%2F4%2B1%2F4\"Simplify right side
\n" ); document.write( "\"4%28x%2B1%2F4%29%5E2=13%2F4\"
\n" ); document.write( "\"4%28x%2B1%2F4%29%5E2=13%2F4\"Subtract 13/4 from both sides\r
\n" ); document.write( "\n" ); document.write( "\"%28cross%284%29%2A%28x%2B1%2F4%29%5E2%29%2Fcross%284%29=%2813%2F4%29%2F4\"Now you can solve for x by first dividing each side by 4
\n" ); document.write( "\"sqrt%28%28x%2B1%2F4%29%5E2%29=sqrt%2813%2F16%29\"Then take the square root of both sides
\n" ); document.write( "\"x%2B1%2F4=0%2B-sqrt%2813%2F16%29\"(ignore the zero before the plus/minus)
\n" ); document.write( "\"x%2B1%2F4=0%2B-sqrt%2813%2F16%29\"finally subtract 1/4 from each side
\n" ); document.write( "\"x=0%2B-sqrt%2813%2F16%29-1%2F4\"remember the square root of a number is both positive and negative
\n" ); document.write( "\"x=0%2B-sqrt%2813%29%2F4-1%2F4\" Add numerators over common denominator
\n" ); document.write( "\"x=%280%2B-sqrt%2813%29-1%29%2F4\"
\n" ); document.write( "So \"x=%28sqrt%2813%29-1%29%2F4\" and \"x=%28-sqrt%2813%29-1%29%2F4\"
\n" ); document.write( "or in decimal form x=0.6514 and x=-1.1514\r
\n" ); document.write( "\n" ); document.write( "Note: the completed square can be verified if you graph both \"4x%5E2%2B2x-3=0\" and \"4%28x%2B1%2F4%29%5E2-13%2F4=0\" together. Set them up in y form (ex \"y=4x%5E2%2B2x-3\") and they should both be the same graph. Hope this helps. \n" ); document.write( "
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