Question

If using the method of completing the square to solve the quadratic equation x^2-5x-18=0x 2 −5x−18=0, which number would have to be added to "complete the square"?

Answer 1

25/4 will have to be added to "complete the square"

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