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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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