Question

Solve for x: -3(x-2)2+17=0 Round your answer to the nearest hundredth. A. x=0.38, -4.38 B. x=3.67, -7.67 C. x=4.38, -0.38 D. x = 7.67, -3.67

Answer 1

C

Explanation:

given

- 3(x - 2)² + 17 = 0 ( subtract 17 from both sides )

- 3(x - 2)² = - 17 ( divide both sides by - 3 )

(x - 2)² =
`(-17)/(-3)` =
`(17)/(3)` ( take square root of both sides )

`√((x-2)^2)` = ±
`\sqrt{(17)/(3) }` , that is

x - 2 = ±
`\sqrt{(17)/(3) }` ( add 2 to both sides )

x = 2 ±
`\sqrt{(17)/(3) }`

Then

x = 2 +
`\sqrt{(17)/(3) }` ≈ 4.38 ( to the nearest hundredth )

x = 2 -
`\sqrt{(17)/(3) }` ≈ - 0.38 ( to the nearest hundredth )