Question

How do I solve `x^2 + 12x = -27` by completing the square?

Answer 1

`x^2+12x=-27`

Take the co-efficient of the middle `x` term and half it

`12/2 =6`

Square that number and add and subtract it from the equation
This gives the perfect square component.

`6^2=36`

`x^2+12x+(36)-(36)=-27`

Then factorise it, the first three terms form a perfect square

`(x+6)^2-36=-27`

Simplify left over numbers

`(x+6)^2=9`

Now we solve for `x`

Square root both sides to get rid of the power

`(x+6)=+-3`
`x=+-3-6`
`x=3-6` or `x=-3-6`
`x=-3` or `x=-9`