Question

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

Answer 1

Answer:

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)