Question

Which of the following is a solution of x2 + 6x = -22? -3+- i sqrt13-3+- i sqrt52-6 +- i sqrt52-6+- i sqrt13

Answer 1

we have

x^2+6x=-22

complete the square

Divide 6 by 2

6/2=3

squared

3^2=9

adds and subtract 9 to the equation

(x^2+6x+9-9)=-22

(x^2+6x+9)=-22+9

rewrite as perfect squares

(x+3)^2=-13

Remember that

i^2=-1

square root both sides

`\begin{gathered} x+3=\pm\sqrt[]{-13} \\ x+3=\pm i\sqrt[]{13} \\ x=-3\pm i\sqrt[]{13} \end{gathered}`