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Simplifying
(2a + 9b)(2a + -9b) = 0
Multiply (2a + 9b) * (2a + -9b)
(2a * (2a + -9b) + 9b * (2a + -9b)) = 0
((2a * 2a + -9b * 2a) + 9b * (2a + -9b)) = 0
Reorder the terms:
((-18ab + 4a2) + 9b * (2a + -9b)) = 0
((-18ab + 4a2) + 9b * (2a + -9b)) = 0
(-18ab + 4a2 + (2a * 9b + -9b * 9b)) = 0
(-18ab + 4a2 + (18ab + -81b2)) = 0
Reorder the terms:
(-18ab + 18ab + 4a2 + -81b2) = 0
Combine like terms: -18ab + 18ab = 0
(0 + 4a2 + -81b2) = 0
(4a2 + -81b2) = 0
Solving
4a2 + -81b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '81b2' to each side of the equation.
4a2 + -81b2 + 81b2 = 0 + 81b2
Combine like terms: -81b2 + 81b2 = 0
4a2 + 0 = 0 + 81b2
4a2 = 0 + 81b2
Remove the zero:
4a2 = 81b2
Divide each side by '4'.
a2 = 20.25b2
Simplifying
a2 = 20.25b2
Take the square root of each side:
a = {-4.5b, 4.5b}
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