Question

Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5
I had no idea what I'm doing so I'd prefer just an easy answer. I need to get this stuff done with

Answer 1

\[\huge\rm 7\sin^2x-14sinx+2=-5\]
set it equal to 0 (add 5 both sides)
\[\large\rm 7\sin^2x-14sinx+2+5=0\]\[\large\rm 7\sin^2x-14sinx+7=0\]
this is just a quadratic equation
let say `sinx=y`\[\large\rm 7y^2-14y+7=0\]
find the solution of this quadratic equation

Answer 2

I don't even know how to do that

Answer 3

you don't know how to solve quadratic equation ?

Answer 4

take out the common factor which is 7\[7(y^2-2y+1)=0\]
\[\large\rm y^2-2y+1=0\]
you can use quadratic formula \[\huge\rm \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]
where a=leading coefficient
b=middle term( coefficient of `x` term)
C= constant
\[\large\rm Ax^2+Bx+C=0\]

Answer 5

7(y^2-2y+1)=0
divide both sides by 7. that's how i got y^2-2y+1=0