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Simplifying
(7a + -4b)(7a + 4b) = 0
Multiply (7a + -4b) * (7a + 4b)
(7a * (7a + 4b) + -4b * (7a + 4b)) = 0
((7a * 7a + 4b * 7a) + -4b * (7a + 4b)) = 0
Reorder the terms:
((28ab + 49a2) + -4b * (7a + 4b)) = 0
((28ab + 49a2) + -4b * (7a + 4b)) = 0
(28ab + 49a2 + (7a * -4b + 4b * -4b)) = 0
(28ab + 49a2 + (-28ab + -16b2)) = 0
Reorder the terms:
(28ab + -28ab + 49a2 + -16b2) = 0
Combine like terms: 28ab + -28ab = 0
(0 + 49a2 + -16b2) = 0
(49a2 + -16b2) = 0
Solving
49a2 + -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.
49a2 + -16b2 + 16b2 = 0 + 16b2
Combine like terms: -16b2 + 16b2 = 0
49a2 + 0 = 0 + 16b2
49a2 = 0 + 16b2
Remove the zero:
49a2 = 16b2
Divide each side by '49'.
a2 = 0.3265306122b2
Simplifying
a2 = 0.3265306122b2
Take the square root of each side:
a = {-0.571428571b, 0.571428571b}
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