How do I complete the square if #f(x) = 3x^2 + 12x - 9#?

Question

10551 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-09-13T22:42:17

Begin by adding 9 to both sides of the equation.

#3x^2+12x=9#

Factor out a #3# from the left side of the equation.

#3(x^2+4x)=9#

Locate the #x# term and take half of the coefficient and square it

#(4/2)^2=2^2=4#

Add #3*4# to the right side of the equation. Because we factored out a #3#.

On the left side add #4# within the parenthesis.

#3(x^2+4x+4)=9+12#, Perfect square trinomial

#3(x+2)^2=9+12#

#3(x+2)^2=21#

#(x+2)^2=7#, Divide by 3

#sqrt((x+2)^2)=sqrt(7)#

#x+2=+-sqrt(7)#

#x=+-sqrt(7)-2#