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Simplifying
(7u + 4v)(7u + -4v) = 0
Multiply (7u + 4v) * (7u + -4v)
(7u * (7u + -4v) + 4v * (7u + -4v)) = 0
((7u * 7u + -4v * 7u) + 4v * (7u + -4v)) = 0
Reorder the terms:
((-28uv + 49u2) + 4v * (7u + -4v)) = 0
((-28uv + 49u2) + 4v * (7u + -4v)) = 0
(-28uv + 49u2 + (7u * 4v + -4v * 4v)) = 0
(-28uv + 49u2 + (28uv + -16v2)) = 0
Reorder the terms:
(-28uv + 28uv + 49u2 + -16v2) = 0
Combine like terms: -28uv + 28uv = 0
(0 + 49u2 + -16v2) = 0
(49u2 + -16v2) = 0
Solving
49u2 + -16v2 = 0
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Add '16v2' to each side of the equation.
49u2 + -16v2 + 16v2 = 0 + 16v2
Combine like terms: -16v2 + 16v2 = 0
49u2 + 0 = 0 + 16v2
49u2 = 0 + 16v2
Remove the zero:
49u2 = 16v2
Divide each side by '49'.
u2 = 0.3265306122v2
Simplifying
u2 = 0.3265306122v2
Take the square root of each side:
u = {-0.571428571v, 0.571428571v}
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