Question

Solve the following quadratic by

completing the square.
y = x² - 4x + 1
X = [?] ± +√[]

Answer 1

x^2 - 4x + 1 = 0

x^2 - 4x + 4 = 3

(x - 2)^2 = 3

x - 2 = +√3

x = 2 + √3

Answer 2

x = 2 ± √3

Explanation:

x² - 4x + 1 = 0

x² - 4x = -1

Divide the co-efficient of x by 2. Co-efficient of x is 4, 4÷ 2 = 2.

Add the square of 2 to both sides. Square of 2 is 4.

x² - 4x + 4 = -1 + 4

x² - 2*2x + 2² = 3

{LHS is in the from a² - 2ab + b² = (a -b)²}

(x - 2)² = 3

Take square root,

x - 2 = ±√3

Add 2 to both sides,

x = 2 ± √3