Question

Question 4 of 10 Which of the following are solutions to the equation below? Check all that apply. x² - 6x+9 = 11 A. X= V2 + 6 B. X = 2 - VG C. X=-11 + 3 D. X= V11 + 3 E. x = 2 + V6 F. X=-3 +6

Answer 1

C. and D.

Explanation:

We have the following equation:

`x^2-6x+9=11`

We solve by obtaining a squared binomial, just like this:

`\begin{gathered} x^2-6x+9-9=11-9 \\ x^2-6x+(-3)^2=2+(-3)^2 \\ (x-3)^2=2+9 \\ x-3=\pm\sqrt[]{11} \\ x=\pm\sqrt[]{11}+3 \\ x_1=\sqrt[]{11}+3 \\ x_2=-\sqrt[]{11}+3 \end{gathered}`

Therefore the solutions are options C. and D.