Question

Which of the following are solutions to the equation below?

Check all that apply.
x2 - 6x + 9 = 11

Answer 1

`\large\boxed{\sf \ \ x = 3+√(11) \ \ or \ \ x = 3-√(11) \ \ }`

Explanation:

Hello,

`x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=√(11) \ or \ x-3=-√(11)\\<=> x = 3+√(11) \ or \ x = 3-√(11)`

Do not hesitate if you have any question

Hope this helps

Answer 2

x = 3 ± sqrt(11)

Explanation:

x^2 - 6x + 9 = 11

Recognizing that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)