Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary.

x2 – x – 7 = 0

Answer 1

x ≈ - 2.193 , x ≈ 3.193

Explanation:

x² - x - 7 = 0 ( add 7 to both sides )

x² - x = 7

to complete the square

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

x² + 2(- 0.5)x + 0.25 = 7 + 0.25

(x - 0.5)² = 7.25 ( take square root of both sides )

x - 0.5 = ±
`√(7.25)` ≈ ± 2.693 ( add 0.5 to both sides )

x = 0.5 ± 2.693

then

x = 0.5 - 2.693 = - 2.193

x = 0.5 + 2.693 = 3.193