Question

X^2-2x=5 solve by completing the square

Answer 1

x = ± sqrt(6) + 1

Explanation:

`x^2 - 2x = 5`

First, add half of -2 squared to both sides:

`x^2 - 2x + (-(2)/(2))^2 = 5 + (-1)^2`

`x^2 - 2x + 1 = 5 + 1`

`x^2 - 2x + 1 = 6`

Then, factor the perfect square trinomial on the left:

`(x - 1)^2 = 6`

Finally, square root both sides:

`√((x - 1)^2) = √(6)`

`x - 1 = √(6)` or
`x - 1 = -√(6)`

x = ± sqrt(6) + 1