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Simplifying
(4w + 7v)(4w + -7v) = 0
Reorder the terms:
(7v + 4w)(4w + -7v) = 0
Reorder the terms:
(7v + 4w)(-7v + 4w) = 0
Multiply (7v + 4w) * (-7v + 4w)
(7v * (-7v + 4w) + 4w * (-7v + 4w)) = 0
((-7v * 7v + 4w * 7v) + 4w * (-7v + 4w)) = 0
Reorder the terms:
((28vw + -49v2) + 4w * (-7v + 4w)) = 0
((28vw + -49v2) + 4w * (-7v + 4w)) = 0
(28vw + -49v2 + (-7v * 4w + 4w * 4w)) = 0
(28vw + -49v2 + (-28vw + 16w2)) = 0
Reorder the terms:
(28vw + -28vw + -49v2 + 16w2) = 0
Combine like terms: 28vw + -28vw = 0
(0 + -49v2 + 16w2) = 0
(-49v2 + 16w2) = 0
Solving
-49v2 + 16w2 = 0
Solving for variable 'v'.
Move all terms containing v to the left, all other terms to the right.
Add '-16w2' to each side of the equation.
-49v2 + 16w2 + -16w2 = 0 + -16w2
Combine like terms: 16w2 + -16w2 = 0
-49v2 + 0 = 0 + -16w2
-49v2 = 0 + -16w2
Remove the zero:
-49v2 = -16w2
Divide each side by '-49'.
v2 = 0.3265306122w2
Simplifying
v2 = 0.3265306122w2
Take the square root of each side:
v = {-0.571428571w, 0.571428571w}
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