Question

Solving quadratic equations with complex solutions x2 + 4x + 8 = 0.

Answer 1

`\large\boxed{x=-2\pm2i}`

Explanation:

`x^2+4x+8=0\qquad\text{subtract 8 from both sides}\\\\x^2+4x+8-8=0-8\\\\x^2+2(x)(2)=-8\qquad\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2(x)(2)+2^2=-8+2^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=-8+4\\\\(x+2)^2=-4\iff x+2=\pm√(-4)\\\\x+2=\pm√((4)(-1))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\x+2=\pm\sqrt4\cdot√(-1)\qquad\text{use}\ √(-1)=i\\\\x+2=\pm2\cdot i\qquad\text{subtract 2 from both sides}\\\\x=-2\pm2i`