Question

Place the following steps in order to complete the square and solve the quadratic equation x2-6x+7=0

Answer 1

The solved expression is
`x=3+√(2)` and
`x=3-√(2)`

Therefore
`x=3\pm√(2)`

Explanation:

Given quadratic equation is
`x^2-6x+7=0`

To solve the given equation by using completing the square :

`x^2-6x+7=0`

Rewritting the above equation as below :

`x^2-6x+7+2-2=0`

`(x^2-6x+7+2)-2=0`

`(x^2-6x+9)-2=0`

`(x^2-6x+3^2)-2=0`

`(x^2-2(x)(3)+3^2)-2=0` ( it is of the form of
`(a-b)^2=a^2-2ab+b^2` heere a=x and b=3 )

`(x-3)^2-2=0`

`(x-3)^2=2`

Taking square root on both sides we get

`√((x-3)^2)=\pm√(2)`

`x-3=\pm√(2)`

`x=\pm√(2)+3`

`x=3\pm√(2)`

Therefore
`x=3+√(2)` and
`x=3-√(2)`