document.write( "Question 189423: Solve for x: x^2 + 7x + 4 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form. \n" ); document.write( "

Algebra.Com's Answer #142119 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2+%2B+7x+%2B+4+=+0\"$
\n" ); document.write( "Subtract $\"4\"$ from both sides
\n" ); document.write( " $\"x%5E2+%2B+7x+=+-4\"$
\n" ); document.write( "Complete the square by taking $\"1%2F2\"$ of the
\n" ); document.write( "coefficient of the $\"x\"$ term, square it, and
\n" ); document.write( "add it to both sides
\n" ); document.write( " $\"x%5E2+%2B+7x+%2B+%287%2F2%29%5E2+=+-4+%2B+%287%2F2%29%5E2\"$
\n" ); document.write( " $\"x%5E2+%2B+7x+%2B+49%2F4+=+-4+%2B+49%2F4\"$
\n" ); document.write( " $\"x%5E2+%2B+7x+%2B+49%2F4+=+-%2816%2F4%29+%2B+49%2F4\"$
\n" ); document.write( " $\"x%5E2+%2B+7x+%2B+49%2F4+=+33%2F4\"$
\n" ); document.write( "The left side is a perfect square. Rewrite it.
\n" ); document.write( " $\"%28x+%2B+7%2F2%29%5E2+=+33%2F4\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"x+%2B+7%2F2+=+sqrt%2833%29%2F2\"$
\n" ); document.write( "and also
\n" ); document.write( " $\"x+%2B+7%2F2+=+-sqrt%2833%29%2F2\"$
\n" ); document.write( "so
\n" ); document.write( " $\"x+=+%28-7+%2B+sqrt%2833%29%29%2F2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=+%28-7+-+sqrt%2833%29%29%2F2\"$
\n" ); document.write( " \n" ); document.write( "

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