help

[modern wyvern]

how does doing that give you =2 because i got upto the part 9sin^2x-6sinx-1=0 however i dont get how you end up with it =2??

[drifting rune]

is this solving?

or js simplifuomg

1 - sin^2 x = 8 sin^2 x - 6 sin x

9 sin^2x - 6 sin x - 1 = 0

let u = sin x

9u^2 - 6u - 1 = 0

lemme try complete the square

acc

3 sin x - 1 squared is 9u^2 - 6u + 1

compared to the other one

you have to minus two and then add on the other side

9u^2 - 6u - 1 = 0

add 2 on both sides

9u^2 - 6u + 1 = 2

(3u - 1)^2 = 2

(3 sin x - 1)^2 = 2

[modern wyvern]

Why

[true sail]

9u^2 - 6u - 1 = 0
(3u - 1)^2 - 1 - 1 = 0

[drifting rune]

9u^2-6u - 1 = 0
9[u^2 - 2/3 u] - 1 = 0
9[(u - 1/3)^2 - 1/9] - 1 = 0

9(u - 1/3)^2 - 1 -1 = 0

9(u - 1/3)^2 = 2

3(u - 1/3) x 3(u - 1/3) = 2

(3u - 1)(3u - 1) = 2

(3u - 1)^2 = 2

(3 sin x - 1)^2 = 2

bravo

@true sail dont ned

[true sail]

😅

[light pendant]

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[drifting rune]

already got it