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Simplifying 135r2 + 2r + -12393 = 0 Reorder the terms: -12393 + 2r + 135r2 = 0 Solving -12393 + 2r + 135r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 135 the coefficient of the squared term: Divide each side by '135'. -91.8 + 0.01481481481r + r2 = 0 Move the constant term to the right: Add '91.8' to each side of the equation. -91.8 + 0.01481481481r + 91.8 + r2 = 0 + 91.8 Reorder the terms: -91.8 + 91.8 + 0.01481481481r + r2 = 0 + 91.8 Combine like terms: -91.8 + 91.8 = 0.0 0.0 + 0.01481481481r + r2 = 0 + 91.8 0.01481481481r + r2 = 0 + 91.8 Combine like terms: 0 + 91.8 = 91.8 0.01481481481r + r2 = 91.8 The r term is 0.01481481481r. Take half its coefficient (0.007407407405). Square it (0.00005486968446) and add it to both sides. Add '0.00005486968446' to each side of the equation. 0.01481481481r + 0.00005486968446 + r2 = 91.8 + 0.00005486968446 Reorder the terms: 0.00005486968446 + 0.01481481481r + r2 = 91.8 + 0.00005486968446 Combine like terms: 91.8 + 0.00005486968446 = 91.80005486968446 0.00005486968446 + 0.01481481481r + r2 = 91.80005486968446 Factor a perfect square on the left side: (r + 0.007407407405)(r + 0.007407407405) = 91.80005486968446 Calculate the square root of the right side: 9.581234517 Break this problem into two subproblems by setting (r + 0.007407407405) equal to 9.581234517 and -9.581234517.Subproblem 1
r + 0.007407407405 = 9.581234517 Simplifying r + 0.007407407405 = 9.581234517 Reorder the terms: 0.007407407405 + r = 9.581234517 Solving 0.007407407405 + r = 9.581234517 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.007407407405' to each side of the equation. 0.007407407405 + -0.007407407405 + r = 9.581234517 + -0.007407407405 Combine like terms: 0.007407407405 + -0.007407407405 = 0.000000000000 0.000000000000 + r = 9.581234517 + -0.007407407405 r = 9.581234517 + -0.007407407405 Combine like terms: 9.581234517 + -0.007407407405 = 9.573827109595 r = 9.573827109595 Simplifying r = 9.573827109595Subproblem 2
r + 0.007407407405 = -9.581234517 Simplifying r + 0.007407407405 = -9.581234517 Reorder the terms: 0.007407407405 + r = -9.581234517 Solving 0.007407407405 + r = -9.581234517 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.007407407405' to each side of the equation. 0.007407407405 + -0.007407407405 + r = -9.581234517 + -0.007407407405 Combine like terms: 0.007407407405 + -0.007407407405 = 0.000000000000 0.000000000000 + r = -9.581234517 + -0.007407407405 r = -9.581234517 + -0.007407407405 Combine like terms: -9.581234517 + -0.007407407405 = -9.588641924405 r = -9.588641924405 Simplifying r = -9.588641924405Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.573827109595, -9.588641924405}
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