Question

Solve the equation by completing the square.

x2 - 4x + 1 = 0
a. 2
b. 2+ 3
C. 21 V15
d. 1

Answer 1

x = 2 +√3, 2 -√3.

Explanation:

x^2 - 4x + 1 = 0

x^2 - 4x = -1

(x - 2)^2 - 4 = -1

(x - 2)^2 = 3

x - 2 = +/-√3

x = 2 +√3, 2 -√3.

Answer 2

b. 2 + √3

Explanation:

x² − 4x + 1 = 0

x² − 4x = -1

To complete the square, take half of -4, square it, and add the result to both sides. (-4/2)² = 4.

x² − 4x + 4 = -1 + 4

(x − 2)² = 3

x − 2 = √3

x = 2 + √3