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Simplifying
(9m + -8w)(9m + 8w) = 0
Multiply (9m + -8w) * (9m + 8w)
(9m * (9m + 8w) + -8w * (9m + 8w)) = 0
((9m * 9m + 8w * 9m) + -8w * (9m + 8w)) = 0
Reorder the terms:
((72mw + 81m2) + -8w * (9m + 8w)) = 0
((72mw + 81m2) + -8w * (9m + 8w)) = 0
(72mw + 81m2 + (9m * -8w + 8w * -8w)) = 0
(72mw + 81m2 + (-72mw + -64w2)) = 0
Reorder the terms:
(72mw + -72mw + 81m2 + -64w2) = 0
Combine like terms: 72mw + -72mw = 0
(0 + 81m2 + -64w2) = 0
(81m2 + -64w2) = 0
Solving
81m2 + -64w2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '64w2' to each side of the equation.
81m2 + -64w2 + 64w2 = 0 + 64w2
Combine like terms: -64w2 + 64w2 = 0
81m2 + 0 = 0 + 64w2
81m2 = 0 + 64w2
Remove the zero:
81m2 = 64w2
Divide each side by '81'.
m2 = 0.7901234568w2
Simplifying
m2 = 0.7901234568w2
Take the square root of each side:
m = {-0.888888889w, 0.888888889w}
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