Rewrite the function by completing the square.

f (x) = x2 + x - 30

x = 5 or x = - 6

Step-by-step explanation:

x² + x - 30 = 0

a = 1

b = 1

c = - 30

Now,

x² + x - 30 = 0

x² + x + (1/2*1) ² - (1/2*1) ² - 30 = 0

x² + x + (1/2) ² - (1/4) - 30 = 0

(x + 1/2) ² - 1/4 - 30 = 0

(x + 1/2) ² - 1 - 120/4 = 0

(x + 1/2) ² - 121/4 = 0

(x + 1/2) ² = 121/4

(x + 1/2) = + -√121/4

(x + 1/2) = + - 11/2

x + 1/2 = + - 11/2

x = - 1/2 + - 11/2

x = - 1/2 + 11/2 or x = - 1/2 - 11/2

x = - 1+11/2 or x = - 1 - 11/2

x = 10/2 or x = - 12/2

x = 5 or x = - 6