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Simplifying
(7u + 6v)(7u + -6v) = 0
Multiply (7u + 6v) * (7u + -6v)
(7u * (7u + -6v) + 6v * (7u + -6v)) = 0
((7u * 7u + -6v * 7u) + 6v * (7u + -6v)) = 0
Reorder the terms:
((-42uv + 49u2) + 6v * (7u + -6v)) = 0
((-42uv + 49u2) + 6v * (7u + -6v)) = 0
(-42uv + 49u2 + (7u * 6v + -6v * 6v)) = 0
(-42uv + 49u2 + (42uv + -36v2)) = 0
Reorder the terms:
(-42uv + 42uv + 49u2 + -36v2) = 0
Combine like terms: -42uv + 42uv = 0
(0 + 49u2 + -36v2) = 0
(49u2 + -36v2) = 0
Solving
49u2 + -36v2 = 0
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Add '36v2' to each side of the equation.
49u2 + -36v2 + 36v2 = 0 + 36v2
Combine like terms: -36v2 + 36v2 = 0
49u2 + 0 = 0 + 36v2
49u2 = 0 + 36v2
Remove the zero:
49u2 = 36v2
Divide each side by '49'.
u2 = 0.7346938776v2
Simplifying
u2 = 0.7346938776v2
Take the square root of each side:
u = {-0.857142857v, 0.857142857v}
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