Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. X^2+2x=17

Answer 1

x ≈ - 5.24 , x ≈ 3.24

Explanation:

x² + 2x = 17

to complete the square

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

x² + 2(1)x + 1 = 17 + 1

(x + 1)² = 18 ( take square root of both sides )

x + 1 = ±
`√(18)` ( subtract 1 from both sides )

x = - 1 ±
`√(18)`

then

x = - 1 -
`√(18)` ≈ - 5.24 ( to the nearest hundredth )

x = - 1 +
`√(18)` ≈ 3.24 ( to the nearest hundredth )