Question

Solve x² - 2x - 23= 0, giving your answers correct to one decimal places ​

Answer 1

x ≈ - 3.9 , x ≈ 5.9

Explanation:

x² - 2x - 23 = 0 ( add 23 to both sides )

x² - 2x = 23

using the method of completing the square

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

x² + 2(- 1)x + 1 = 23 + 1

(x - 1)² = 24 ( take square root of both sides )

x - 1 = ±
`√(24)` ( add 1 to both sides )

x = 1 ±
`√(24)`

then

x = 1 -
`√(24)` ≈ - 3.9 ( to 1 dec. place )

x = 1 +
`√(24)` ≈ 5.9 ( to 1 dec. place )