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Simplifying
(8a + 5b)(8a + -5b) = 0
Multiply (8a + 5b) * (8a + -5b)
(8a * (8a + -5b) + 5b * (8a + -5b)) = 0
((8a * 8a + -5b * 8a) + 5b * (8a + -5b)) = 0
Reorder the terms:
((-40ab + 64a2) + 5b * (8a + -5b)) = 0
((-40ab + 64a2) + 5b * (8a + -5b)) = 0
(-40ab + 64a2 + (8a * 5b + -5b * 5b)) = 0
(-40ab + 64a2 + (40ab + -25b2)) = 0
Reorder the terms:
(-40ab + 40ab + 64a2 + -25b2) = 0
Combine like terms: -40ab + 40ab = 0
(0 + 64a2 + -25b2) = 0
(64a2 + -25b2) = 0
Solving
64a2 + -25b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '25b2' to each side of the equation.
64a2 + -25b2 + 25b2 = 0 + 25b2
Combine like terms: -25b2 + 25b2 = 0
64a2 + 0 = 0 + 25b2
64a2 = 0 + 25b2
Remove the zero:
64a2 = 25b2
Divide each side by '64'.
a2 = 0.390625b2
Simplifying
a2 = 0.390625b2
Take the square root of each side:
a = {-0.625b, 0.625b}
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