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Simplifying
(10xyz + -0.5uv)(10xyz + 0.5uv) = 0
Reorder the terms:
(-0.5uv + 10xyz)(10xyz + 0.5uv) = 0
Reorder the terms:
(-0.5uv + 10xyz)(0.5uv + 10xyz) = 0
Multiply (-0.5uv + 10xyz) * (0.5uv + 10xyz)
(-0.5uv * (0.5uv + 10xyz) + 10xyz * (0.5uv + 10xyz)) = 0
((0.5uv * -0.5uv + 10xyz * -0.5uv) + 10xyz * (0.5uv + 10xyz)) = 0
Reorder the terms:
((-5uvxyz + -0.25u2v2) + 10xyz * (0.5uv + 10xyz)) = 0
((-5uvxyz + -0.25u2v2) + 10xyz * (0.5uv + 10xyz)) = 0
(-5uvxyz + -0.25u2v2 + (0.5uv * 10xyz + 10xyz * 10xyz)) = 0
(-5uvxyz + -0.25u2v2 + (5uvxyz + 100x2y2z2)) = 0
Reorder the terms:
(-5uvxyz + 5uvxyz + -0.25u2v2 + 100x2y2z2) = 0
Combine like terms: -5uvxyz + 5uvxyz = 0
(0 + -0.25u2v2 + 100x2y2z2) = 0
(-0.25u2v2 + 100x2y2z2) = 0
Solving
-0.25u2v2 + 100x2y2z2 = 0
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Add '-100x2y2z2' to each side of the equation.
-0.25u2v2 + 100x2y2z2 + -100x2y2z2 = 0 + -100x2y2z2
Combine like terms: 100x2y2z2 + -100x2y2z2 = 0
-0.25u2v2 + 0 = 0 + -100x2y2z2
-0.25u2v2 = 0 + -100x2y2z2
Remove the zero:
-0.25u2v2 = -100x2y2z2
Divide each side by '-0.25v2'.
u2 = 400v-2x2y2z2
Simplifying
u2 = 400v-2x2y2z2
Take the square root of each side:
u = {-20v-1xyz, 20v-1xyz}
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