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Simplifying
(10u + v)(10u + -1v) = 0
Multiply (10u + v) * (10u + -1v)
(10u * (10u + -1v) + v(10u + -1v)) = 0
((10u * 10u + -1v * 10u) + v(10u + -1v)) = 0
Reorder the terms:
((-10uv + 100u2) + v(10u + -1v)) = 0
((-10uv + 100u2) + v(10u + -1v)) = 0
(-10uv + 100u2 + (10u * v + -1v * v)) = 0
(-10uv + 100u2 + (10uv + -1v2)) = 0
Reorder the terms:
(-10uv + 10uv + 100u2 + -1v2) = 0
Combine like terms: -10uv + 10uv = 0
(0 + 100u2 + -1v2) = 0
(100u2 + -1v2) = 0
Solving
100u2 + -1v2 = 0
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Add 'v2' to each side of the equation.
100u2 + -1v2 + v2 = 0 + v2
Combine like terms: -1v2 + v2 = 0
100u2 + 0 = 0 + v2
100u2 = 0 + v2
Remove the zero:
100u2 = v2
Divide each side by '100'.
u2 = 0.01v2
Simplifying
u2 = 0.01v2
Take the square root of each side:
u = {-0.1v, 0.1v}
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