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Simplifying 14r2 + -21r + -6 = 0 Reorder the terms: -6 + -21r + 14r2 = 0 Solving -6 + -21r + 14r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.4285714286 + -1.5r + r2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1.5r + 0.4285714286 + r2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1.5r + r2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1.5r + r2 = 0 + 0.4285714286 -1.5r + r2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1.5r + r2 = 0.4285714286 The r term is -1.5r. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5r + 0.5625 + r2 = 0.4285714286 + 0.5625 Reorder the terms: 0.5625 + -1.5r + r2 = 0.4285714286 + 0.5625 Combine like terms: 0.4285714286 + 0.5625 = 0.9910714286 0.5625 + -1.5r + r2 = 0.9910714286 Factor a perfect square on the left side: (r + -0.75)(r + -0.75) = 0.9910714286 Calculate the square root of the right side: 0.995525705 Break this problem into two subproblems by setting (r + -0.75) equal to 0.995525705 and -0.995525705.Subproblem 1
r + -0.75 = 0.995525705 Simplifying r + -0.75 = 0.995525705 Reorder the terms: -0.75 + r = 0.995525705 Solving -0.75 + r = 0.995525705 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + r = 0.995525705 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + r = 0.995525705 + 0.75 r = 0.995525705 + 0.75 Combine like terms: 0.995525705 + 0.75 = 1.745525705 r = 1.745525705 Simplifying r = 1.745525705Subproblem 2
r + -0.75 = -0.995525705 Simplifying r + -0.75 = -0.995525705 Reorder the terms: -0.75 + r = -0.995525705 Solving -0.75 + r = -0.995525705 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + r = -0.995525705 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + r = -0.995525705 + 0.75 r = -0.995525705 + 0.75 Combine like terms: -0.995525705 + 0.75 = -0.245525705 r = -0.245525705 Simplifying r = -0.245525705Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.745525705, -0.245525705}
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