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Simplifying
(7a + -3b)(7a + 3b) = 0
Multiply (7a + -3b) * (7a + 3b)
(7a * (7a + 3b) + -3b * (7a + 3b)) = 0
((7a * 7a + 3b * 7a) + -3b * (7a + 3b)) = 0
Reorder the terms:
((21ab + 49a2) + -3b * (7a + 3b)) = 0
((21ab + 49a2) + -3b * (7a + 3b)) = 0
(21ab + 49a2 + (7a * -3b + 3b * -3b)) = 0
(21ab + 49a2 + (-21ab + -9b2)) = 0
Reorder the terms:
(21ab + -21ab + 49a2 + -9b2) = 0
Combine like terms: 21ab + -21ab = 0
(0 + 49a2 + -9b2) = 0
(49a2 + -9b2) = 0
Solving
49a2 + -9b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9b2' to each side of the equation.
49a2 + -9b2 + 9b2 = 0 + 9b2
Combine like terms: -9b2 + 9b2 = 0
49a2 + 0 = 0 + 9b2
49a2 = 0 + 9b2
Remove the zero:
49a2 = 9b2
Divide each side by '49'.
a2 = 0.1836734694b2
Simplifying
a2 = 0.1836734694b2
Take the square root of each side:
a = {-0.428571429b, 0.428571429b}
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