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Simplifying
(8a + 7c)(8a + -7c) = 0
Multiply (8a + 7c) * (8a + -7c)
(8a * (8a + -7c) + 7c * (8a + -7c)) = 0
((8a * 8a + -7c * 8a) + 7c * (8a + -7c)) = 0
Reorder the terms:
((-56ac + 64a2) + 7c * (8a + -7c)) = 0
((-56ac + 64a2) + 7c * (8a + -7c)) = 0
(-56ac + 64a2 + (8a * 7c + -7c * 7c)) = 0
(-56ac + 64a2 + (56ac + -49c2)) = 0
Reorder the terms:
(-56ac + 56ac + 64a2 + -49c2) = 0
Combine like terms: -56ac + 56ac = 0
(0 + 64a2 + -49c2) = 0
(64a2 + -49c2) = 0
Solving
64a2 + -49c2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '49c2' to each side of the equation.
64a2 + -49c2 + 49c2 = 0 + 49c2
Combine like terms: -49c2 + 49c2 = 0
64a2 + 0 = 0 + 49c2
64a2 = 0 + 49c2
Remove the zero:
64a2 = 49c2
Divide each side by '64'.
a2 = 0.765625c2
Simplifying
a2 = 0.765625c2
Take the square root of each side:
a = {-0.875c, 0.875c}
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