Question

2.

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 3x – 12 = 0

A. 3.12, 3.77
B. –12.75, 15.75
C. 5.27, –2.27
D. 4.74, –1.74

Answer 1

C

Explanation:

Given

x² - 3x - 12 = 0 ( add 12 to both sides )

x² - 3x = 12

To complete the square

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

x² + 2(-
`(3)/(2)` )x +
`(9)/(4)` = 12 +
`(9)/(4)`

(x -
`(3)/(2)` )² =
`(57)/(4)` ( take the square root of both sides )

x -
`(3)/(2)` = ±
`\sqrt{(57)/(4) }` = ±
`(√(57) )/(2)` ( add
`(3)/(2)` to both sides )

x =
`(3)/(2)` ±
`(√(57) )/(2)`

Then

x =
`(3)/(2)` +
`(√(57) )/(2)` ≈ 5.27 ( to the nearest hundredth )

x =
`(3)/(2)` -
`(√(57) )/(2)` ≈ - 2.27 ( to the nearest hundredth )