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Simplifying
(2r + 5t)(2r + -5t) = 0
Multiply (2r + 5t) * (2r + -5t)
(2r * (2r + -5t) + 5t * (2r + -5t)) = 0
((2r * 2r + -5t * 2r) + 5t * (2r + -5t)) = 0
Reorder the terms:
((-10rt + 4r2) + 5t * (2r + -5t)) = 0
((-10rt + 4r2) + 5t * (2r + -5t)) = 0
(-10rt + 4r2 + (2r * 5t + -5t * 5t)) = 0
(-10rt + 4r2 + (10rt + -25t2)) = 0
Reorder the terms:
(-10rt + 10rt + 4r2 + -25t2) = 0
Combine like terms: -10rt + 10rt = 0
(0 + 4r2 + -25t2) = 0
(4r2 + -25t2) = 0
Solving
4r2 + -25t2 = 0
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '25t2' to each side of the equation.
4r2 + -25t2 + 25t2 = 0 + 25t2
Combine like terms: -25t2 + 25t2 = 0
4r2 + 0 = 0 + 25t2
4r2 = 0 + 25t2
Remove the zero:
4r2 = 25t2
Divide each side by '4'.
r2 = 6.25t2
Simplifying
r2 = 6.25t2
Take the square root of each side:
r = {-2.5t, 2.5t}
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