Mathematics: Solve x2 + 12x + 6 = 0 using the completing-the-square method. (2 points)

Solve x2 + 12x + 6 = 0 using the completing-the-square

Ответ:

shainaanderson24

12.03.2022

$\large\boxed{x=-6\pm\sqrt{30}}$

Step-by-step explanation:

$(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+12x+6=0\qquad\text{subtract 6 from both sides}\\\\x^2+2(x)(6)=-6\qquad\text{add}\ 6^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(6)+6^2}_{(*)}=-6+6^2\\\\(x+6)^2=-6+36\\\\(x+6)^2=30\Rightarrow x+6=\pm\sqrt{30}\qquad\text{subtract 6 from both sides}\\\\x=-6\pm\sqrt{30}$