Question

Solve the equation by completing the

square. Enter the smallest solution first
and round to the nearest tenth.
s2 - 10s - 23 = 0
-
s = [?]
=

Answer 1

s ≈ - 1.9 , s ≈ 11.9

Explanation:

s² - 10s - 23 = 0 ( add 23 to both sides )

s² - 10s = 23

To complete the square

add ( half the coefficient of the s- term )² to both sides

s² + 2(- 5)s + 25 = 23 + 25

(s - 5)² = 48 ( take square root of both sides )

s - 5 = ±
`√(48)` ( add 5 to both sides )

s = 5 ±
`√(48)`

Then

s = 5 -
`√(48)` ≈ - 1.9 ( to the nearest tenth ) ← smaller solution

s = 5 +
`√(48)` ≈ 11.9 ( to the nearest tenth ) ← larger solution