To simplify this expression, we can rewrite it in terms of sine and cosine using the identity sin^2(x) + cos^2(x) = 1.
We have: 7sin^2(x) - 5sin(x)cos(x) - cos^2(x) = 0
Replacing sin^2(x) with 1 - cos^2(x), we get:
7(1 - cos^2(x)) - 5sin(x)cos(x) - cos^2(x) = 0
Expanding, we get:
7 - 7cos^2(x) - 5sin(x)cos(x) - cos^2(x) = 0
Rewriting this expression in terms of sin(2x) using the identity sin(2x) = 2sin(x)cos(x), we get:
7 - 7cos^2(x) - 5sin(2x) - cos^2(x) = 0
Combining like terms, we get:
-8cos^2(x) - 5sin(2x) + 7 = 0
Therefore, the simplified expression is: -8cos^2(x) - 5sin(2x) + 7 = 0.
To simplify this expression, we can rewrite it in terms of sine and cosine using the identity sin^2(x) + cos^2(x) = 1.
We have: 7sin^2(x) - 5sin(x)cos(x) - cos^2(x) = 0
Replacing sin^2(x) with 1 - cos^2(x), we get:
7(1 - cos^2(x)) - 5sin(x)cos(x) - cos^2(x) = 0
Expanding, we get:
7 - 7cos^2(x) - 5sin(x)cos(x) - cos^2(x) = 0
Rewriting this expression in terms of sin(2x) using the identity sin(2x) = 2sin(x)cos(x), we get:
7 - 7cos^2(x) - 5sin(2x) - cos^2(x) = 0
Combining like terms, we get:
-8cos^2(x) - 5sin(2x) + 7 = 0
Therefore, the simplified expression is: -8cos^2(x) - 5sin(2x) + 7 = 0.