Question

Solve by completing the square. 9x=3x2−1

Answer 1

x = 3/2 + √(31/12) or x = 3/2 - √(31/12)

Explanation:

9x = 3x² − 1

3x² - 9x - 1 = 0

3x² - 9x = 1

x² - 3x = 1/3

x² - 3x + (3/2)² = 1/3 + (3/2)²

(x - 3/2)² = 4/12 + 27/12

(x - 3/2)² = 31/12

x - 3/2 = √(31/12) or x - 3/2 = -√(31/12)

x = 3/2 + √(31/12) or x = 3/2 - √(31/12)