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Simplifying
(3a + -5b)(3a + 5b) = 0
Multiply (3a + -5b) * (3a + 5b)
(3a * (3a + 5b) + -5b * (3a + 5b)) = 0
((3a * 3a + 5b * 3a) + -5b * (3a + 5b)) = 0
Reorder the terms:
((15ab + 9a2) + -5b * (3a + 5b)) = 0
((15ab + 9a2) + -5b * (3a + 5b)) = 0
(15ab + 9a2 + (3a * -5b + 5b * -5b)) = 0
(15ab + 9a2 + (-15ab + -25b2)) = 0
Reorder the terms:
(15ab + -15ab + 9a2 + -25b2) = 0
Combine like terms: 15ab + -15ab = 0
(0 + 9a2 + -25b2) = 0
(9a2 + -25b2) = 0
Solving
9a2 + -25b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '25b2' to each side of the equation.
9a2 + -25b2 + 25b2 = 0 + 25b2
Combine like terms: -25b2 + 25b2 = 0
9a2 + 0 = 0 + 25b2
9a2 = 0 + 25b2
Remove the zero:
9a2 = 25b2
Divide each side by '9'.
a2 = 2.777777778b2
Simplifying
a2 = 2.777777778b2
Take the square root of each side:
a = {-1.666666667b, 1.666666667b}
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