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Simplifying
(8a + -2b)(8a + 2b) = 0
Multiply (8a + -2b) * (8a + 2b)
(8a * (8a + 2b) + -2b * (8a + 2b)) = 0
((8a * 8a + 2b * 8a) + -2b * (8a + 2b)) = 0
Reorder the terms:
((16ab + 64a2) + -2b * (8a + 2b)) = 0
((16ab + 64a2) + -2b * (8a + 2b)) = 0
(16ab + 64a2 + (8a * -2b + 2b * -2b)) = 0
(16ab + 64a2 + (-16ab + -4b2)) = 0
Reorder the terms:
(16ab + -16ab + 64a2 + -4b2) = 0
Combine like terms: 16ab + -16ab = 0
(0 + 64a2 + -4b2) = 0
(64a2 + -4b2) = 0
Solving
64a2 + -4b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '4b2' to each side of the equation.
64a2 + -4b2 + 4b2 = 0 + 4b2
Combine like terms: -4b2 + 4b2 = 0
64a2 + 0 = 0 + 4b2
64a2 = 0 + 4b2
Remove the zero:
64a2 = 4b2
Divide each side by '64'.
a2 = 0.0625b2
Simplifying
a2 = 0.0625b2
Take the square root of each side:
a = {-0.25b, 0.25b}
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