# Solve the quadratic equation by completing the square: x^2 - 4x - 11 = 0

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The equation x^2 - 4x - 11 = 0 has to be solved by completion of squares.

x^2 - 4x - 11 = 0

=> x^2 - 4x = 11

=> x^2 - 4x + 4 = 11 + 4

=> (x - 2)^2 = 15

x - 2 = `sqrt 15` and x - 2 = `-sqrt 15`

=> x = `2 + sqrt 15` and x = `2 - sqrt 15`

**The solution of the equation x^2 - 4x - 11 = 0 is `2+- sqrt 15` **

`x^2-4x-11=0`

`Delta = 16- 4(1)(-11)=60>0`

has two differents real solutions

`x=(4+-2sqrt(15))/2=2+-sqrt(15)`