Conplete the square to solve the quadratic equation. x 1 {x}^(2) - 6x + 12 = 2x + 20

Question

Conplete the square to solve the quadratic equation. x


`1 {x}^(2) - 6x + 12 = 2x + 20`

Answer 1

`\large\boxed{x=4\pm2\sqrt6}`

Explanation:

`x^2-6x+12=2x+20\qquad\text{subtract}\ 2x\ \text{and}\ 12\ \text{from both sides}\\\\x^2-8x=8\\\\x^2-2(x)(4)=8\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=8+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=24\iff x-4=\pm√(24)\\\\x-4=\pm√(4\cdot6)\\\\x-4=\pm\sqrt4\cdot\sqrt6\\\\x-4=\pm2\sqrt6\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt6`