Question

Solve by completing the square.

s2 + 22s = 27

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

Answer 1

s = 1.17, -23.17

Explanation:

s^2 + 22s = 27

Take the coefficient of s

22

Divide by 2

22/2 =11

Square it

11^2 =121

Add this to both sides

s^2 + 22s+121 = 27+121

s^2 + 22s+121 = 148

(s+11)^2 = 148

Take the square root of each side

sqrt((s+11)^2) = ±sqrt(148)

s+11 = ±sqrt(148)

Subtract 11 from each side

s+11-11 = -11 ±sqrt(148)

s = -11 ±sqrt(148)

s = -11 + sqrt(148) = 1.1655

- 11 - sqrt(148)=-23.166

Rounding to the nearest hundredth

s = 1.17, -23.17