If 5x^2-2x+10=0 then (x-1/2)^2=?

Morningfox

If 5x^2-2x+10=0 , then x = 0.2 +/- 1.4 i. So then (x - 1/2)^2 = -1.87 +/- 0.84 i

la console

5x² - 2x + 10 = 0 5x² - 2x = - 10 x² - (2/5).x = - 2 x² - (2/5).x + (1/5)² = - 2 + (1/5)² x² - (2/5).x + (1/5)² = - (50/25) + (1/25) x² - (2/5).x + (1/5)² = - 49/25 x² - (2/5).x + (1/5)² = (49/25).i² [x - (1/5)]² = [± (7/5).i]² x - (1/5) = ± (7/5).i x = (1/5) ± [(7/5).i] x = (1 ± 7i)/5 When: x = (1 + 7i)/5 [x - (1/2)]² = [(1 + 7i)/5 - (1/2)]² [x - (1/2)]² = [(2 + 14i - 5)/10]² [x - (1/2)]² = [(- 3 + 14i)/10]² [x - (1/2)]² = (- 3 + 14i)²/100 [x - (1/2)]² = (9 - 84i + 196i)/100 → where: i² = - 1 [x - (1/2)]² = (- 187 - 84i)/100 When : x = (1 - 7i)/5 [x - (1/2)]² = [(1 - 7i)/5 - (1/2)]² [x - (1/2)]² = [(2 - 14i - 5)/10]² [x - (1/2)]² = [(- 3 - 14i)/10]² [x - (1/2)]² = (- 3 - 14i)²/100 [x - (1/2)]² = (9 + 84i + 196i)/100 → where: i² = - 1 [x - (1/2)]² = (- 187 + 84i)/100 Conclusion: [x - (1/2)]² = (- 187 ± 84i)/100

az_lender

x = 2/10 +/- (1/10)*sqrt(4 - 200) = 0.2 +/- 1.4i. x - 1/2 = -0.3 +/- 1.4i; (x - 1/2)^2 = 0.9 +/- 0.42i - 1.96 = -1.06 +/- 0.42i.