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

1 Answer

6 votes

Answer:


\large\boxed{x=-6\pm√(30)}

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√(30)\qquad\text{subtract 6 from both sides}\\\\x=-6\pm√(30)

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