document.write( "Question 52395: x^2+4x+7=0 find all real solutions and express in a+bi \n" ); document.write( "
Algebra.Com's Answer #34934 by Nate(3500)\"\" \"About 
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x^2 + 4x + 7 = 0
\n" ); document.write( "x^2 + 4x = -7
\n" ); document.write( "(x + 2)^2 = 4 - 7 = -3
\n" ); document.write( "x + 2 = +- sqrt(3)i
\n" ); document.write( "x = -2 +- sqrt(3)i
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B4x%2B7+=+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%2A1%2A7=-12\".
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\n" ); document.write( " The discriminant -12 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -12 is + or - \"sqrt%28+12%29+=+3.46410161513775\".
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\n" ); document.write( " The solution is
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\n" ); document.write( " Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B7+%29\"
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