Solved Quadratic Equation Results in Imaginary Roots

Topic : Quadratic Equation

Question : Solve x² - 2x + 3 = 0

Solution :
x² - 2x + 3 = 0
to find the roots let us consider equation as,
x² - 2x + 3 +1 -1 = 0
x² - 2x +1 + 3 -1 = 0
x² - 2x +1 + 2 = 0 --------- (1)
if a = x and b= 1
by (a-b)² = a² -2ab + b²
(x - 1)² = x² -2(x)(1) + (1)
(x - 1)² = x² -2x + 1
So, replace x² -2x + 1 by (x - 1)² in equation (1)
then,
(x - 1)² + 2 = 0
(x - 1)² = -2
x - 1 = √-2
x - 1 = √2 *√-1
x - 1 = √2 i (because √-1 = i :imaginary unit)
x = √2 i + 1 or 1 + √2