Question

What are the solutions to 3x2 + 12x +6=0 ?

Answer 1

`\large\boxed{x=-2-\sqrt2\ or\ x=-2+\sqrt2}`

Explanation:

`3x^2+12x+6=0\qquad\text{divide both sides by 3}\\\\(3x^2)/(3)+(12x)/(3)+(6)/(3)=(0)/(3)\\\\x^2+4x+2=0\qquad\text{subtract 2 from both sides}\\\\x^2+4x+2-2=0-2\\\\x^2+4x=-2\\\\x^2+2(x)(2)=-2\qquad\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2(x)(2)+2^2=-2+2^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=-2+4\\\\(x+2)^2=2\iff x+2=\pm\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-2\pm\sqrt2`