Question

(17 POINTS) Which number should be added to both sides of this quadratic equation to complete the square?

Answer 1

(b/2)² + 1 = x² - 3x + (b/2)²

b²/4 + 1 = x² - 3x + b²/4

b²/4 - b²/4 = x² - 3x - 1

x² - 3x - 1 = 0

x² - 3x = 1

x² - 3x + 9/4 = 1 + 9/4

(x - 3/2)² = 13/4

x - 3/2 = ±(√13/4)

x = ±√13/2 + 3/2

so the number that must be added will be 3/2