You can put this solution on YOUR website!
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:
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.
Your equation already has the variables on one side and the constant term on the other.
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.
3. Calculate half of the "non-squared" term.
Half of 7 is 7/2.
4. Square the half.
5. Add the square to both sides:
6. Rewrite the variable side as a perfect square (using the half from step 3):
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!)
(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:
Subtracting 7/2 from each side of each equation we get:
which simplify to:
c = -3 or c = -4
You are welcome to check the answers.