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Simplifying
(11a + 4b)(11a + -4b) = 0
Multiply (11a + 4b) * (11a + -4b)
(11a * (11a + -4b) + 4b * (11a + -4b)) = 0
((11a * 11a + -4b * 11a) + 4b * (11a + -4b)) = 0
Reorder the terms:
((-44ab + 121a2) + 4b * (11a + -4b)) = 0
((-44ab + 121a2) + 4b * (11a + -4b)) = 0
(-44ab + 121a2 + (11a * 4b + -4b * 4b)) = 0
(-44ab + 121a2 + (44ab + -16b2)) = 0
Reorder the terms:
(-44ab + 44ab + 121a2 + -16b2) = 0
Combine like terms: -44ab + 44ab = 0
(0 + 121a2 + -16b2) = 0
(121a2 + -16b2) = 0
Solving
121a2 + -16b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '16b2' to each side of the equation.
121a2 + -16b2 + 16b2 = 0 + 16b2
Combine like terms: -16b2 + 16b2 = 0
121a2 + 0 = 0 + 16b2
121a2 = 0 + 16b2
Remove the zero:
121a2 = 16b2
Divide each side by '121'.
a2 = 0.132231405b2
Simplifying
a2 = 0.132231405b2
Take the square root of each side:
a = {-0.363636364b, 0.363636364b}
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