Solve x 2 - 4x - 7 = 0 by completing the square. What are the solutions?

x = 2±sqrt (11)

Step-by-step explanation:

x^2 - 4x - 7 = 0

Add 7 to each side

x^2 - 4x - 7+7 = 0+7

x^2 - 4x = 7

To complete the square take the coefficient of the x term and divide by 2 and then square it. Add it to both sides

-4 / 2 = - 2 then square

(-2) ^2 = 4

Add 4 to both sides

x^2 - 4x+4 = 7+4

x^2 - 4x+4 = 11

Factor the left side into (x-b/2) ^2

(x-2) ^2 = 11

Take the square root of each side

sqrt ((x-2) ^2) = ±sqrt (11)

x-2 = ±sqrt (11)

Add to to each side

x-2+2 = 2±sqrt (11)

x = 2±sqrt (11)