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Simplifying 3r2 + -44r + 120 = 0 Reorder the terms: 120 + -44r + 3r2 = 0 Solving 120 + -44r + 3r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 40 + -14.66666667r + r2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -14.66666667r + -40 + r2 = 0 + -40 Reorder the terms: 40 + -40 + -14.66666667r + r2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -14.66666667r + r2 = 0 + -40 -14.66666667r + r2 = 0 + -40 Combine like terms: 0 + -40 = -40 -14.66666667r + r2 = -40 The r term is -14.66666667r. Take half its coefficient (-7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. -14.66666667r + 53.77777780 + r2 = -40 + 53.77777780 Reorder the terms: 53.77777780 + -14.66666667r + r2 = -40 + 53.77777780 Combine like terms: -40 + 53.77777780 = 13.7777778 53.77777780 + -14.66666667r + r2 = 13.7777778 Factor a perfect square on the left side: (r + -7.333333335)(r + -7.333333335) = 13.7777778 Calculate the square root of the right side: 3.711842912 Break this problem into two subproblems by setting (r + -7.333333335) equal to 3.711842912 and -3.711842912.Subproblem 1
r + -7.333333335 = 3.711842912 Simplifying r + -7.333333335 = 3.711842912 Reorder the terms: -7.333333335 + r = 3.711842912 Solving -7.333333335 + r = 3.711842912 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + r = 3.711842912 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + r = 3.711842912 + 7.333333335 r = 3.711842912 + 7.333333335 Combine like terms: 3.711842912 + 7.333333335 = 11.045176247 r = 11.045176247 Simplifying r = 11.045176247Subproblem 2
r + -7.333333335 = -3.711842912 Simplifying r + -7.333333335 = -3.711842912 Reorder the terms: -7.333333335 + r = -3.711842912 Solving -7.333333335 + r = -3.711842912 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + r = -3.711842912 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + r = -3.711842912 + 7.333333335 r = -3.711842912 + 7.333333335 Combine like terms: -3.711842912 + 7.333333335 = 3.621490423 r = 3.621490423 Simplifying r = 3.621490423Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.045176247, 3.621490423}
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