document.write( "Question 223957: I need help solving this quadratic equation: \"4x%5E2%2B8x%2B2=0\" \n" ); document.write( "
Algebra.Com's Answer #167351 by nerdybill(7384)\"\" \"About 
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\"4x%5E2%2B8x%2B2=0\"
\n" ); document.write( "First, determine whether there is anything common among all three terms -- yes, they all have the common multiple of 2. Therefore, divide both sides by 2 to get:
\n" ); document.write( "\"2x%5E2%2B4x%2B1=0\"
\n" ); document.write( "Since we can't factor, we must resort to the quadratic equation.
\n" ); document.write( "Doing so yields:
\n" ); document.write( "x = {-0.293, -1.707}
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\n" ); document.write( "Details of the quadratic equation to follow:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"2x%5E2%2B4x%2B1+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%284%29%5E2-4%2A2%2A1=8\".
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\n" ); document.write( " Discriminant d=8 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-4%2B-sqrt%28+8+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%284%29%2Bsqrt%28+8+%29%29%2F2%5C2+=+-0.292893218813452\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%284%29-sqrt%28+8+%29%29%2F2%5C2+=+-1.70710678118655\"
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\n" ); document.write( " Quadratic expression \"2x%5E2%2B4x%2B1\" can be factored:
\n" ); document.write( " \"2x%5E2%2B4x%2B1+=+2%28x--0.292893218813452%29%2A%28x--1.70710678118655%29\"
\n" ); document.write( " Again, the answer is: -0.292893218813452, -1.70710678118655.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B1+%29\"

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