Question

x^2+6x=-11

Answer 1

\(\Large\color{black}{ \bf x^2+6x=-11 }\)
\(\Large\color{red}{ \bf ~~~~+11~~~~+11 }\)

\(\Large\color{black}{ \bf x^2+6x+11=0 }\)
imaginary solution

Answer 2

To create a trinomial square on the left-hand side of the equation, add a value to both sides of the equation that is equal to the square of half the coefficient of x. In this problem, add (3)2 to both sides of the equation.

x2+6x+9=−11+9

Simplify the equation.

x2+6x+9=−2

Factor the perfect trinomial square into (x+3)2.

(x+3)2=−2

Solve the equation for x.

More Detail
\[x= -3+i \sqrt{2}, -3-i \sqrt{2}\]

Answer 3

You can use completing the square. It's my favorite one.


\(\Large\color{black}{ \bf x^2+6x=-11 }\)

\(\Large\color{black}{ \bf x^2+6x+9=-11 +9 }\)

\(\Large\color{black}{ \bf x^2+6x+9=-2 }\)

\(\Large\color{black}{ \bf (x+3)^2=-2 }\)

\(\Large\color{black}{ \bf (x+3)=± \sqrt{-2} }\)

\(\Large\color{black}{ \bf x=± \sqrt{-2}~ -3 }\)

Answer 4

Same @SolomonZelman I love completing the square

Answer 5

:)

Answer 6

Thank you so much :D

Answer 7

Anytime !