Question 612138
{{{ c^2+7c=-12 }}}
To complete a square:<ol><li>Gather the variable terms on one side and the constant term on the other side.</li><li>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.)</li><li>Calculate half of the coefficient of the "non-squared" term.</li><li>Calculate the square of the half from step 3.</li><li>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.)</li><li>The side of the equation with the variables is now a perfect square. Rewrite it as:
{{{(x + h)^2}}}
where the "x" is the variable in the equation and "h" is the half you calculated in step 3.</li></ol>Let's see this in action.
1. Gather...
Your equation already has the variables on one side and the constant term on the other.<br>
2. Factor out the coefficient if it is not 1.
The coefficient of your squared term is a 1 so we can ignore this step.<br>
3. Calculate half of the "non-squared" term.
Half of 7 is 7/2.<br>
4. Square the half.
{{{(7/2)^2 = 49/4}}}<br>
5. Add the square to both sides:
{{{ c^2+7c + 49/4=-12 + 49/4 }}}
{{{ c^2+7c + 49/4=-48/4 + 49/4 }}}
{{{ c^2+7c + 49/4=1/4 }}}
6. Rewrite the variable side as a perfect square (using the half from step 3):
{{{(c + 7/2)^2 = 1/4}}}<br>
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!)
{{{sqrt((c + 7/2)^2) = sqrt(1/4)}}}
{{{c + 7/2 = 0 +- 1/2}}}
(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.)
In long form this is:
{{{c + 7/2 = 1/2}}} or {{{c + 7/2 = -1/2}}}
Subtracting 7/2 from each side of each equation we get:
{{{c = -6/2}}} or {{{c = -8/2}}}
which simplify to:
c = -3 or c = -4<br>
You are welcome to check the answers.