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

1 Answer
Aug 29, 2014

#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#