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Simplifying
(6r + 5s)(6r + -5s) = 0
Multiply (6r + 5s) * (6r + -5s)
(6r * (6r + -5s) + 5s * (6r + -5s)) = 0
((6r * 6r + -5s * 6r) + 5s * (6r + -5s)) = 0
Reorder the terms:
((-30rs + 36r2) + 5s * (6r + -5s)) = 0
((-30rs + 36r2) + 5s * (6r + -5s)) = 0
(-30rs + 36r2 + (6r * 5s + -5s * 5s)) = 0
(-30rs + 36r2 + (30rs + -25s2)) = 0
Reorder the terms:
(-30rs + 30rs + 36r2 + -25s2) = 0
Combine like terms: -30rs + 30rs = 0
(0 + 36r2 + -25s2) = 0
(36r2 + -25s2) = 0
Solving
36r2 + -25s2 = 0
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '25s2' to each side of the equation.
36r2 + -25s2 + 25s2 = 0 + 25s2
Combine like terms: -25s2 + 25s2 = 0
36r2 + 0 = 0 + 25s2
36r2 = 0 + 25s2
Remove the zero:
36r2 = 25s2
Divide each side by '36'.
r2 = 0.6944444444s2
Simplifying
r2 = 0.6944444444s2
Take the square root of each side:
r = {-0.833333333s, 0.833333333s}
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