Question

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation? {–7, 1} {1, 7}

Answer 1

`\large\boxed{\{-7,\ 1\}}`

Explanation:

`x^2+6x=7\\\\x^2+2(x)(3)=7\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\x^2+2(x)(3)+3^2=7+9\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=16\Rightarrow x+3=\pm√(16)\\\\x+3=-4\ \vee\ x+3=4\qquad\text{subtract 3 from both sides}\\\\x=-7\ \vee\ x=1`