# How do you solve #3x^2+12x+81=15# by completing the square?

##### 1 Answer

Jun 30, 2017

#### Explanation:

Note that all of the terms are divisible by

#x^2+4x+27=5#

To make the left hand side into a perfect square, subtract

#x^2+4x+4 = -22#

The left hand side is now

#(x+2)^2 = -22#

The square of any real number is non-negative, so this quadratic equation only has non-real complex solutions.

If you want to proceed further, note that if

#sqrt(-n) = i sqrt(n)#

where

So we find:

#(x+2)^2 = (i sqrt(22))^2#

and hence:

#x+2 = +-i sqrt(22)#

Subtracting

#x = -2+-i sqrt(22)#