document.write( "Question 42506: Find the constant term that should be added to make the following expression a perfect-square trinomial.\r
\n" ); document.write( "\n" ); document.write( "x^2 + 7x\r
\n" ); document.write( "\n" ); document.write( "Is it 49? \n" ); document.write( "

Algebra.Com's Answer #27627 by Nate(3500) $\"\"$ $\"About$

You can put this solution on YOUR website!
x^2 + 7x + k
\n" ); document.write( "(x + 3.5)(x + 3.5) is what we want
\n" ); document.write( "xx + 3.5x + 3.5x + 12.25
\n" ); document.write( "x^2 + 7x + 12.25
\n" ); document.write( "k = 12.25
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B7x%2B12.25+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%287%29%5E2-4%2A1%2A12.25=0\"$ .
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\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: $\"x+=+%28-%287%29%29%2F2%5C1\"$ .
\n" ); document.write( " Expression can be factored: $\"1x%5E2%2B7x%2B12.25+=+1%28x--3.5%29%2A%28x--3.5%29\"$
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\n" ); document.write( " Again, the answer is: -3.5, -3.5.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B12.25+%29\"$

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