Question

Solve by completing the square

6x-x^2-7

Answer 1

`x=\{3+\sqrt 2,\:\:3-\sqrt 2\}`

Explanation:

`6x-x^2-7=0\\x^2-6x +7=0\\x^2-2.3.x +3^2=3^2-7\\(x-3)^2=9-7\\\huge\boxed{(x-3)^2=2}...(square\: completed)\\x-3=\pm√(2) \\x=3+\pm√(2)\\\therefore x =3+√(2)\: or \: x =3-√(2)\\\therefore x =\{3+√(2),\:\:3-√(2)\}\\`

Answer 2

Hi there!

The completed square is -(x - 3) ^2 + 2

Hope this helps !