Question

Solve 5x^2 - 7x+2 -0 by completing the square. What are the solutions?

Answer 1

5x² - 7x + 2 = 0

5(x² - 7/5 x) + 2 = 0

5(x² - 7/5 x + 49/100 - 49/100) + 2 = 0

5(x² - 2 • 7/10 x + (7/10)²) - 49/20 + 2 = 0

5(x - 7/10)² - 9/20 = 0

5(x - 7/10)² = 9/20

(x - 7/10)² = 9/100

x - 7/10 = ± √(9/100)

x - 7/10 = ± 3/10

x = 7/10 ± 3/10

x = 10/10 = 1   or   x = 4/10 = 2/5