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Simplifying 13r2 + 24r + -320 = 0 Reorder the terms: -320 + 24r + 13r2 = 0 Solving -320 + 24r + 13r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -24.61538462 + 1.846153846r + r2 = 0 Move the constant term to the right: Add '24.61538462' to each side of the equation. -24.61538462 + 1.846153846r + 24.61538462 + r2 = 0 + 24.61538462 Reorder the terms: -24.61538462 + 24.61538462 + 1.846153846r + r2 = 0 + 24.61538462 Combine like terms: -24.61538462 + 24.61538462 = 0.00000000 0.00000000 + 1.846153846r + r2 = 0 + 24.61538462 1.846153846r + r2 = 0 + 24.61538462 Combine like terms: 0 + 24.61538462 = 24.61538462 1.846153846r + r2 = 24.61538462 The r term is 1.846153846r. Take half its coefficient (0.923076923). Square it (0.8520710058) and add it to both sides. Add '0.8520710058' to each side of the equation. 1.846153846r + 0.8520710058 + r2 = 24.61538462 + 0.8520710058 Reorder the terms: 0.8520710058 + 1.846153846r + r2 = 24.61538462 + 0.8520710058 Combine like terms: 24.61538462 + 0.8520710058 = 25.4674556258 0.8520710058 + 1.846153846r + r2 = 25.4674556258 Factor a perfect square on the left side: (r + 0.923076923)(r + 0.923076923) = 25.4674556258 Calculate the square root of the right side: 5.046529067 Break this problem into two subproblems by setting (r + 0.923076923) equal to 5.046529067 and -5.046529067.Subproblem 1
r + 0.923076923 = 5.046529067 Simplifying r + 0.923076923 = 5.046529067 Reorder the terms: 0.923076923 + r = 5.046529067 Solving 0.923076923 + r = 5.046529067 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.923076923' to each side of the equation. 0.923076923 + -0.923076923 + r = 5.046529067 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + r = 5.046529067 + -0.923076923 r = 5.046529067 + -0.923076923 Combine like terms: 5.046529067 + -0.923076923 = 4.123452144 r = 4.123452144 Simplifying r = 4.123452144Subproblem 2
r + 0.923076923 = -5.046529067 Simplifying r + 0.923076923 = -5.046529067 Reorder the terms: 0.923076923 + r = -5.046529067 Solving 0.923076923 + r = -5.046529067 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.923076923' to each side of the equation. 0.923076923 + -0.923076923 + r = -5.046529067 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + r = -5.046529067 + -0.923076923 r = -5.046529067 + -0.923076923 Combine like terms: -5.046529067 + -0.923076923 = -5.96960599 r = -5.96960599 Simplifying r = -5.96960599Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.123452144, -5.96960599}
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