Question

Solve for x by completing the square. Show your work and round to the nearest tenth if necessary.

x² - 18x = 65

Answer 1

`\sf\\x^2-18x=65\\or,\ x^2-2.x.9+9^2=65+9^2\\or,\ (x-9)^2=146\\or,\ x-9=\pm √(146)\\or,\ x=9\pm√(146)\\or,\ x\approx 21.1,-3.1`

Answer 2

x = - 3.1 , x = 21.1

Explanation:

x² - 18x = 65

to complete the square

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

x² + 2(- 9)x + 81 = 65 + 81

(x - 9)² = 146 ( take square root of both sides )

`√((x-9)^2)` = ±
`√(146)`

x - 9 = ± 12.1 ( to the nearest tenth )

add 9 to both sides

x = 9 ± 12.1

Then

x = 9 - 12 .1 = - 3.1

x = 9 + 12.1 = 21.1