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Simplifying
(6v + 5f)(6v + -5f) = 0
Reorder the terms:
(5f + 6v)(6v + -5f) = 0
Reorder the terms:
(5f + 6v)(-5f + 6v) = 0
Multiply (5f + 6v) * (-5f + 6v)
(5f * (-5f + 6v) + 6v * (-5f + 6v)) = 0
((-5f * 5f + 6v * 5f) + 6v * (-5f + 6v)) = 0
Reorder the terms:
((30fv + -25f2) + 6v * (-5f + 6v)) = 0
((30fv + -25f2) + 6v * (-5f + 6v)) = 0
(30fv + -25f2 + (-5f * 6v + 6v * 6v)) = 0
(30fv + -25f2 + (-30fv + 36v2)) = 0
Reorder the terms:
(30fv + -30fv + -25f2 + 36v2) = 0
Combine like terms: 30fv + -30fv = 0
(0 + -25f2 + 36v2) = 0
(-25f2 + 36v2) = 0
Solving
-25f2 + 36v2 = 0
Solving for variable 'f'.
Move all terms containing f to the left, all other terms to the right.
Add '-36v2' to each side of the equation.
-25f2 + 36v2 + -36v2 = 0 + -36v2
Combine like terms: 36v2 + -36v2 = 0
-25f2 + 0 = 0 + -36v2
-25f2 = 0 + -36v2
Remove the zero:
-25f2 = -36v2
Divide each side by '-25'.
f2 = 1.44v2
Simplifying
f2 = 1.44v2
Take the square root of each side:
f = {-1.2v, 1.2v}
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