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Simplifying
(2b + -5c)(2b + 5c) = 0
Multiply (2b + -5c) * (2b + 5c)
(2b * (2b + 5c) + -5c * (2b + 5c)) = 0
((2b * 2b + 5c * 2b) + -5c * (2b + 5c)) = 0
Reorder the terms:
((10bc + 4b2) + -5c * (2b + 5c)) = 0
((10bc + 4b2) + -5c * (2b + 5c)) = 0
(10bc + 4b2 + (2b * -5c + 5c * -5c)) = 0
(10bc + 4b2 + (-10bc + -25c2)) = 0
Reorder the terms:
(10bc + -10bc + 4b2 + -25c2) = 0
Combine like terms: 10bc + -10bc = 0
(0 + 4b2 + -25c2) = 0
(4b2 + -25c2) = 0
Solving
4b2 + -25c2 = 0
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '25c2' to each side of the equation.
4b2 + -25c2 + 25c2 = 0 + 25c2
Combine like terms: -25c2 + 25c2 = 0
4b2 + 0 = 0 + 25c2
4b2 = 0 + 25c2
Remove the zero:
4b2 = 25c2
Divide each side by '4'.
b2 = 6.25c2
Simplifying
b2 = 6.25c2
Take the square root of each side:
b = {-2.5c, 2.5c}
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