Complete the square: x2 – 6x + = –13 +

solve by  completing the square.

x2+6x+13=0

move the constant to the right side by subtracting 13 from each side.

x2+6x=−13

divide the coefficient of the  x  term by  2.

x2+6x=−13

62=3

square the result and add it to both sides.

32=9

x2+6x+9=−13+9

factor the left side and simplify the right side.

(x+3)(x+3)=−4

rewrite as the square of the binomial. note that the  3  in the binomial is the same value  3  that resulted from dividing the coefficient of the  x  term by  2.

(x+3)2=−4

square root both sides and solve for  x.

√(x+3)2=√−4

x+3=±2i

x=−3±2i