Question

solve the equation by completing square method

2x^2 -2√2x + 1​

Answer 1

Answer:

Given equation is 2x²-2√2x+1= 0

Divide both sides by 2

x² - √2x + 1/2 = 0

x² - 2(√2/2)x + 1/2 = 0

a=2, b=-2(√2/2), c=1

Add (b/2)² = 1/2 on both sides

x² - 2(√2/2)x + 1 + 1/2 = 1/2

(x)² - 2(1)(-√2/2) + 1 + (-√2/2)² = 1/2

(x)² - 2(1)(-√2/2) + (-√2/2)² = 1/2 - 1

[x-(-√2/2)]² = -1/2

x-(-√2/2) = √(-1/2) = (√2)i/2

x = (√2)i/2 - (√2)/2 = (√2) [i - 1]/2