document.write( "Question 612138: please solve this problem by completing the square
\n" ); document.write( " $\"+c%28squared%29%2B7c=-12+\"$ \n" ); document.write( "

Algebra.Com's Answer #385418 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+c%5E2%2B7c=-12+\"$
\n" ); document.write( "To complete a square:

Gather the variable terms on one side and the constant term on the other side.
If the coefficient of the squared term is not a 1, factor it out. (Since none of the problems you posted have a coefficient that is not 1, we can ignore this step (and its consequences to the remaining steps) until we do have such a coefficient.)
Calculate half of the coefficient of the \"non-squared\" term.
Calculate the square of the half from step 3.
Add the square from step 4 to each side of the equation. (Note: This step is slightly different if a coefficient was factored out in step 2.)
The side of the equation with the variables is now a perfect square. Rewrite it as:
\n" ); document.write( " $\"%28x+%2B+h%29%5E2\"$
\n" ); document.write( "where the \"x\" is the variable in the equation and \"h\" is the half you calculated in step 3.

Let's see this in action.
\n" ); document.write( "1. Gather...
\n" ); document.write( "Your equation already has the variables on one side and the constant term on the other.

\n" ); document.write( "2. Factor out the coefficient if it is not 1.
\n" ); document.write( "The coefficient of your squared term is a 1 so we can ignore this step.

\n" ); document.write( "3. Calculate half of the \"non-squared\" term.
\n" ); document.write( "Half of 7 is 7/2.

\n" ); document.write( "4. Square the half.
\n" ); document.write( " $\"%287%2F2%29%5E2+=+49%2F4\"$

\n" ); document.write( "5. Add the square to both sides:
\n" ); document.write( " $\"+c%5E2%2B7c+%2B+49%2F4=-12+%2B+49%2F4+\"$
\n" ); document.write( " $\"+c%5E2%2B7c+%2B+49%2F4=-48%2F4+%2B+49%2F4+\"$
\n" ); document.write( " $\"+c%5E2%2B7c+%2B+49%2F4=1%2F4+\"$
\n" ); document.write( "6. Rewrite the variable side as a perfect square (using the half from step 3):
\n" ); document.write( " $\"%28c+%2B+7%2F2%29%5E2+=+1%2F4\"$

\n" ); document.write( "With the completed square we can now proceed to a solution. The next step is to find the square root of each side. (Don't forget the negative square root!)
\n" ); document.write( " $\"sqrt%28%28c+%2B+7%2F2%29%5E2%29+=+sqrt%281%2F4%29\"$
\n" ); document.write( " $\"c+%2B+7%2F2+=+0+%2B-+1%2F2\"$
\n" ); document.write( "(Note; Algebra.com's formula soltware will not let me us a \"plus or minus\" symbol without something in front of it. This is why the zero is there. The zero is mathematically unnecessary.)
\n" ); document.write( "In long form this is:
\n" ); document.write( " $\"c+%2B+7%2F2+=+1%2F2\"$ or $\"c+%2B+7%2F2+=+-1%2F2\"$
\n" ); document.write( "Subtracting 7/2 from each side of each equation we get:
\n" ); document.write( " $\"c+=+-6%2F2\"$ or $\"c+=+-8%2F2\"$
\n" ); document.write( "which simplify to:
\n" ); document.write( "c = -3 or c = -4

\n" ); document.write( "You are welcome to check the answers. \n" ); document.write( "

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