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Simplifying
(13a + 11c)(13a + -11c) = 0
Multiply (13a + 11c) * (13a + -11c)
(13a * (13a + -11c) + 11c * (13a + -11c)) = 0
((13a * 13a + -11c * 13a) + 11c * (13a + -11c)) = 0
Reorder the terms:
((-143ac + 169a2) + 11c * (13a + -11c)) = 0
((-143ac + 169a2) + 11c * (13a + -11c)) = 0
(-143ac + 169a2 + (13a * 11c + -11c * 11c)) = 0
(-143ac + 169a2 + (143ac + -121c2)) = 0
Reorder the terms:
(-143ac + 143ac + 169a2 + -121c2) = 0
Combine like terms: -143ac + 143ac = 0
(0 + 169a2 + -121c2) = 0
(169a2 + -121c2) = 0
Solving
169a2 + -121c2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '121c2' to each side of the equation.
169a2 + -121c2 + 121c2 = 0 + 121c2
Combine like terms: -121c2 + 121c2 = 0
169a2 + 0 = 0 + 121c2
169a2 = 0 + 121c2
Remove the zero:
169a2 = 121c2
Divide each side by '169'.
a2 = 0.7159763314c2
Simplifying
a2 = 0.7159763314c2
Take the square root of each side:
a = {-0.846153846c, 0.846153846c}
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