document.write( "Question 169644: \"3x%5E2=-12x-1\" solve using the quadratic formula. I can do the first few steps. I am completely lost on the math involved between the last two steps. \n" ); document.write( "
Algebra.Com's Answer #125021 by Alan3354(69443)\"\" \"About 
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solve using the quadratic formula. I can do the first few steps. I am completely lost on the math involved between the last two steps.
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\n" ); document.write( "\"3x%5E2=-12x-1\"
\n" ); document.write( "\"3x%5E2%2B12x%2B1+=+0\"
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"3x%5E2%2B12x%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=%2812%29%5E2-4%2A3%2A1=132\".
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\n" ); document.write( " Discriminant d=132 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-12%2B-sqrt%28+132+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+132+%29%29%2F2%5C3+=+-0.0851457844873238\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%2812%29-sqrt%28+132+%29%29%2F2%5C3+=+-3.91485421551268\"
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\n" ); document.write( " Quadratic expression \"3x%5E2%2B12x%2B1\" can be factored:
\n" ); document.write( " \"3x%5E2%2B12x%2B1+=+%28x--0.0851457844873238%29%2A%28x--3.91485421551268%29\"
\n" ); document.write( " Again, the answer is: -0.0851457844873238, -3.91485421551268.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B12%2Ax%2B1+%29\"

\n" ); document.write( "\n" ); document.write( "Ignore what the solver says about the factors, it's not right unless the coefficient of the x^2 term is 1.
\n" ); document.write( "The solutions are:
\n" ); document.write( "-2 + sqrt(33)/3
\n" ); document.write( "-2 - sqrt(33)/3\r
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