Question

Solve x2 - 8x+ 8 = 0 by completing the square,

Answer 1

`x_(1) =4+2√(2)\\x_(2)=4-2√(2)`

Explanation:

`x^(2)` - 8x+ 8 = 0

we divide the coefficient of the X by half :

in this case: 8x/2 = 4 , then we do the following

to the result obtained (4) squared: 4^2=16

we sum and subtract by 16 to maintain the balance of equation:

`x^(2)` - 8x+ 16-16+8 = 0

we have:

`(x-4)^(2)` -16 +8=0

`(x-4)^(2)` =16-8

`(x-4)^(2)` = 8

we write the square root on both sides of the equation:

`\sqrt{(x-4)^(2)} = √(8)`

we know:

`\sqrt{a^(2)} = abs(a)`

so we have:

abs(x-4)=
`\sqrt{2^(2)2 }`

abs(x-4)=2
`√(2)`

we have:

`x_(1) -4 = 2√(2) \\\\x_(2) -4 =- 2√(2)`

finally we have:

`x_(1) = 4+2√(2) \\\\x_(2) =4 - 2√(2)`