Question

Solve the following quadratic by
completing the square.
y = x2 - 4x + 1

Answer 1

y = (x - 2)² - 3

y = 0 if x = 2+√3 or 2-√3

Explanation:

`y = x^2 - 4x + 1\\\\y = \underline{x^2 - 2\cdot x\cdot2+2^2}-2^2 +1\\\\y=(x-2)^2-4+1 \\\\y=(x-2)^2-3\\\\\\y=0\quad\iff\quad(x-2)^2-3=0\\\\(x-2)^2=3\\\\x-2=\pm\sqrt3\\\\x=2\pm\sqrt3`