Question

Solve this quadratic equation by completing the square.x² + 6x = 18A. x=-6± √√27OB. x=-6±√18OC. x=-3± √27OD. x=-318

Answer 1

Consider that to complete the square it is necessary to add 9 both sides:

$\begin{gathered} x^2+6x+9=18+9 \\ (x+3)^2=27 \\ (x+3)^2-27=0 \end{gathered}$

Then, you have a difference of squares, whose factorization is:

$(x+3)^2-27=(x+3+\sqrt[\placeholder{⬚}]{27})(x+3-\sqrt[\placeholder{⬚}]{27})=0$

Then, the solutions for x are (by making each factor equal to zero):

$x=-3\pm\sqrt[\placeholder{⬚}]{27}$

Hence, the answer is option C.