SOLUTION: Find all solutions to the equation. 7 sin^2x - 14 sin x + 2 = -5 Show all your work.

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Question 1086811: Find all solutions to the equation.
7 sin^2x - 14 sin x + 2 = -5
Show all your work.

Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
u=sin%28x%29
So,
7u%5E2-14u%2B2=-5
7u%5E2-14u-7=0
u%5E2-2u-1=0
Complete the square,
%28u%5E2-2u%2B1%29-1=1
%28u-1%29%5E2=2
u-1=0+%2B-+sqrt%282%29
u=1+%2B-+sqrt%282%29
sin%28x%29=1+%2B-+sqrt%282%29
The positive solution yields no solutions since sin%28x%29%3C=1
So,
sin%28x%29=1-sqrt%282%29
x=sin%5E%28-1%29%281-sqrt%282%29%29
Remember there are two solutions.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions to the equation.
7 sin^2x - 14 sin x + 2 = -5
Show all your work. 
7+%2A+sin+%28x%29%5E2+-+14+%2A+sin+%28x%29+%2B+2+=+-+5 

7+%2A+sin+%28x%29%5E2+-+14+%2A+sin+%28x%29+%2B+7+=+0 -------- Adding 5 to both sides

7%28sin+%28x%29%5E2+-+2+%2A+sin+%28x%29+%2B+1%29+=+7%280%29 ---- Factoring out GCF, 7

sin+%28x%29%5E2+-+2+%2A+sin+%28x%29+%2B+1+=+0

(sin x - 1)(sin x - 1) = 0, or %28sin+%28x%29+-+1%29%5E2+=+0 -------- Factoring TRINOMIAL

Now, solve for sin x 

You continue and SHOW YOUR WORK!

IGNORE all other RIDICULOUS answers!