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Simplifying 11r2 + -12r + -13 = 0 Reorder the terms: -13 + -12r + 11r2 = 0 Solving -13 + -12r + 11r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.181818182 + -1.090909091r + r2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + -1.090909091r + 1.181818182 + r2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + -1.090909091r + r2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + -1.090909091r + r2 = 0 + 1.181818182 -1.090909091r + r2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 -1.090909091r + r2 = 1.181818182 The r term is -1.090909091r. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091r + 0.2975206612 + r2 = 1.181818182 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091r + r2 = 1.181818182 + 0.2975206612 Combine like terms: 1.181818182 + 0.2975206612 = 1.4793388432 0.2975206612 + -1.090909091r + r2 = 1.4793388432 Factor a perfect square on the left side: (r + -0.5454545455)(r + -0.5454545455) = 1.4793388432 Calculate the square root of the right side: 1.216280742 Break this problem into two subproblems by setting (r + -0.5454545455) equal to 1.216280742 and -1.216280742.Subproblem 1
r + -0.5454545455 = 1.216280742 Simplifying r + -0.5454545455 = 1.216280742 Reorder the terms: -0.5454545455 + r = 1.216280742 Solving -0.5454545455 + r = 1.216280742 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + r = 1.216280742 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + r = 1.216280742 + 0.5454545455 r = 1.216280742 + 0.5454545455 Combine like terms: 1.216280742 + 0.5454545455 = 1.7617352875 r = 1.7617352875 Simplifying r = 1.7617352875Subproblem 2
r + -0.5454545455 = -1.216280742 Simplifying r + -0.5454545455 = -1.216280742 Reorder the terms: -0.5454545455 + r = -1.216280742 Solving -0.5454545455 + r = -1.216280742 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + r = -1.216280742 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + r = -1.216280742 + 0.5454545455 r = -1.216280742 + 0.5454545455 Combine like terms: -1.216280742 + 0.5454545455 = -0.6708261965 r = -0.6708261965 Simplifying r = -0.6708261965Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.7617352875, -0.6708261965}
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