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Simplifying
(7r + 4t)(7r + -4t) = 0
Multiply (7r + 4t) * (7r + -4t)
(7r * (7r + -4t) + 4t * (7r + -4t)) = 0
((7r * 7r + -4t * 7r) + 4t * (7r + -4t)) = 0
Reorder the terms:
((-28rt + 49r2) + 4t * (7r + -4t)) = 0
((-28rt + 49r2) + 4t * (7r + -4t)) = 0
(-28rt + 49r2 + (7r * 4t + -4t * 4t)) = 0
(-28rt + 49r2 + (28rt + -16t2)) = 0
Reorder the terms:
(-28rt + 28rt + 49r2 + -16t2) = 0
Combine like terms: -28rt + 28rt = 0
(0 + 49r2 + -16t2) = 0
(49r2 + -16t2) = 0
Solving
49r2 + -16t2 = 0
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '16t2' to each side of the equation.
49r2 + -16t2 + 16t2 = 0 + 16t2
Combine like terms: -16t2 + 16t2 = 0
49r2 + 0 = 0 + 16t2
49r2 = 0 + 16t2
Remove the zero:
49r2 = 16t2
Divide each side by '49'.
r2 = 0.3265306122t2
Simplifying
r2 = 0.3265306122t2
Take the square root of each side:
r = {-0.571428571t, 0.571428571t}
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