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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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