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Simplifying 81R2 + -137.68R + 10.498 = 0 Reorder the terms: 10.498 + -137.68R + 81R2 = 0 Solving 10.498 + -137.68R + 81R2 = 0 Solving for variable 'R'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.1296049383 + -1.699753086R + R2 = 0 Move the constant term to the right: Add '-0.1296049383' to each side of the equation. 0.1296049383 + -1.699753086R + -0.1296049383 + R2 = 0 + -0.1296049383 Reorder the terms: 0.1296049383 + -0.1296049383 + -1.699753086R + R2 = 0 + -0.1296049383 Combine like terms: 0.1296049383 + -0.1296049383 = 0.0000000000 0.0000000000 + -1.699753086R + R2 = 0 + -0.1296049383 -1.699753086R + R2 = 0 + -0.1296049383 Combine like terms: 0 + -0.1296049383 = -0.1296049383 -1.699753086R + R2 = -0.1296049383 The R term is -1.699753086R. Take half its coefficient (-0.849876543). Square it (0.7222901383) and add it to both sides. Add '0.7222901383' to each side of the equation. -1.699753086R + 0.7222901383 + R2 = -0.1296049383 + 0.7222901383 Reorder the terms: 0.7222901383 + -1.699753086R + R2 = -0.1296049383 + 0.7222901383 Combine like terms: -0.1296049383 + 0.7222901383 = 0.5926852 0.7222901383 + -1.699753086R + R2 = 0.5926852 Factor a perfect square on the left side: (R + -0.849876543)(R + -0.849876543) = 0.5926852 Calculate the square root of the right side: 0.769860507 Break this problem into two subproblems by setting (R + -0.849876543) equal to 0.769860507 and -0.769860507.Subproblem 1
R + -0.849876543 = 0.769860507 Simplifying R + -0.849876543 = 0.769860507 Reorder the terms: -0.849876543 + R = 0.769860507 Solving -0.849876543 + R = 0.769860507 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '0.849876543' to each side of the equation. -0.849876543 + 0.849876543 + R = 0.769860507 + 0.849876543 Combine like terms: -0.849876543 + 0.849876543 = 0.000000000 0.000000000 + R = 0.769860507 + 0.849876543 R = 0.769860507 + 0.849876543 Combine like terms: 0.769860507 + 0.849876543 = 1.61973705 R = 1.61973705 Simplifying R = 1.61973705Subproblem 2
R + -0.849876543 = -0.769860507 Simplifying R + -0.849876543 = -0.769860507 Reorder the terms: -0.849876543 + R = -0.769860507 Solving -0.849876543 + R = -0.769860507 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '0.849876543' to each side of the equation. -0.849876543 + 0.849876543 + R = -0.769860507 + 0.849876543 Combine like terms: -0.849876543 + 0.849876543 = 0.000000000 0.000000000 + R = -0.769860507 + 0.849876543 R = -0.769860507 + 0.849876543 Combine like terms: -0.769860507 + 0.849876543 = 0.080016036 R = 0.080016036 Simplifying R = 0.080016036Solution
The solution to the problem is based on the solutions from the subproblems. R = {1.61973705, 0.080016036}
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