Question

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

Answer 1

The solutions are
`x=2(+/-)√(11)`

Explanation:

we have

`x^(2)-4x-7=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`x^(2)-4x=7`

Complete the square. Remember to balance the equation by adding the same constants to each side

`x^(2)-4x+4=7+4`

`x^(2)-4x+4=11`

Rewrite as perfect squares

`(x-2)^(2)=11`

Take square root both sides

`x-2=(+/-)√(11)`

`x=2(+/-)√(11)`