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Simplifying
(7a + 8w)(7a + -8w) = 0
Multiply (7a + 8w) * (7a + -8w)
(7a * (7a + -8w) + 8w * (7a + -8w)) = 0
((7a * 7a + -8w * 7a) + 8w * (7a + -8w)) = 0
Reorder the terms:
((-56aw + 49a2) + 8w * (7a + -8w)) = 0
((-56aw + 49a2) + 8w * (7a + -8w)) = 0
(-56aw + 49a2 + (7a * 8w + -8w * 8w)) = 0
(-56aw + 49a2 + (56aw + -64w2)) = 0
Reorder the terms:
(-56aw + 56aw + 49a2 + -64w2) = 0
Combine like terms: -56aw + 56aw = 0
(0 + 49a2 + -64w2) = 0
(49a2 + -64w2) = 0
Solving
49a2 + -64w2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '64w2' to each side of the equation.
49a2 + -64w2 + 64w2 = 0 + 64w2
Combine like terms: -64w2 + 64w2 = 0
49a2 + 0 = 0 + 64w2
49a2 = 0 + 64w2
Remove the zero:
49a2 = 64w2
Divide each side by '49'.
a2 = 1.306122449w2
Simplifying
a2 = 1.306122449w2
Take the square root of each side:
a = {-1.142857143w, 1.142857143w}
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