Question

Solve the equation by completing the square. x^2+2x=17​

Answer 1

`\large\boxed{x=-1\pm3\sqrt2}`

Explanation:

`x^2+2x=17\\\\x^2+2(x)(1)=17\qquad\text{add}\ 1^2=1\ \text{to both sides}\\\\x^2+2(x)(1)+1^2=17+1\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=18\Rightarrow x+1=\pm√(18)\\\\x+1=\pm√(9\cdot2)\\\\x+1=\pm\sqrt9\cdot\sqrt2\\\\x+1=\pm3\sqrt2\qquad\text{subtract 1 from both sides}\\\\x=-1\pm3\sqrt2`