Answer:
25/4 will have to be added to "complete the square"
Step-by-step explanation:
x² - 5x - 18 = 0
x² - 5x = 18
Find the half of the coefficient of x and square it
(5/2)² = 25/4
Add 25/4 to both sides to complete the square
x² - 5x + 25/4 = 18 + 25/4
x² - 5x + 25/4 = 18(4/4) + 25/4
x² - 5x + 25/4 = 72/4 + 25/4
x² - 5x + 25/4 = (72+25)/4
x² - 5x + 25/4 = 97/4
(x - 5/2)² = 97/4
Find the square root of both sides
√(x - 5/2)² = ±√97/4
x - 5/2 = √97/2
x = √97/2 + 5/2 or x = -√97/2 + 5/2
x = 7.42443 or -2.42443
