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Simplifying
(2a + 5b)(2a + -5b) = 0
Multiply (2a + 5b) * (2a + -5b)
(2a * (2a + -5b) + 5b * (2a + -5b)) = 0
((2a * 2a + -5b * 2a) + 5b * (2a + -5b)) = 0
Reorder the terms:
((-10ab + 4a2) + 5b * (2a + -5b)) = 0
((-10ab + 4a2) + 5b * (2a + -5b)) = 0
(-10ab + 4a2 + (2a * 5b + -5b * 5b)) = 0
(-10ab + 4a2 + (10ab + -25b2)) = 0
Reorder the terms:
(-10ab + 10ab + 4a2 + -25b2) = 0
Combine like terms: -10ab + 10ab = 0
(0 + 4a2 + -25b2) = 0
(4a2 + -25b2) = 0
Solving
4a2 + -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.
4a2 + -25b2 + 25b2 = 0 + 25b2
Combine like terms: -25b2 + 25b2 = 0
4a2 + 0 = 0 + 25b2
4a2 = 0 + 25b2
Remove the zero:
4a2 = 25b2
Divide each side by '4'.
a2 = 6.25b2
Simplifying
a2 = 6.25b2
Take the square root of each side:
a = {-2.5b, 2.5b}
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