Question

How do you solve by completing the square: `c²-36= -4c`?

Answer 1

• First, we Transpose the Constant to one side of the equation.
  Transposing `-36` to the other side we get:
  `c^2+4c = 36`

• Application of `(a+b)^2 = a^2 + 2ab + b^2`
  We look at the Co-efficient of `c`. It's `4`
  We take half of this number (including the sign), giving us `2`
  We square this value to get `(2)^2 = 4`. We add this number to BOTH sides of the Equation.
  `c^2+4c+4 = 36+4`
  `c^2+4c+4 = 40`
  The Left Hand side `c^2+4c+4` is in the form `a^2 + 2ab + b^2`
  where `a` is `c`, and `b` is `2`

• The equation can be written as
  `(c+2)^2 = 40`

So `(c+2)` can take either `2sqrt10` or `-2sqrt10` as a value. That's because squaring both will give us 40.

`c+2 = 2sqrt10` (or) `c+2 = -2sqrt10`
`c = 2sqrt10-2` (or) `c = -2sqrt10-2`
`c = 2(sqrt10-1)` (or) `c = -2(sqrt10+1)`

• Solution : `c = 2(sqrt10-1) , -2(sqrt10+1)`

• Verify your answer by substituting these values in the Original Equation `c^2- 36 = -4c`. You will see that the solution is correct.