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Simplifying 0.3r + -0.01 = -0.64r2 Reorder the terms: -0.01 + 0.3r = -0.64r2 Solving -0.01 + 0.3r = -0.64r2 Solving for variable 'r'. Combine like terms: -0.64r2 + 0.64r2 = 0.00 -0.01 + 0.3r + 0.64r2 = 0.00 Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. -0.015625 + 0.46875r + r2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + 0.46875r + 0.015625 + r2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + 0.46875r + r2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + 0.46875r + r2 = 0 + 0.015625 0.46875r + r2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 0.46875r + r2 = 0.015625 The r term is 0.46875r. Take half its coefficient (0.234375). Square it (0.05493164063) and add it to both sides. Add '0.05493164063' to each side of the equation. 0.46875r + 0.05493164063 + r2 = 0.015625 + 0.05493164063 Reorder the terms: 0.05493164063 + 0.46875r + r2 = 0.015625 + 0.05493164063 Combine like terms: 0.015625 + 0.05493164063 = 0.07055664063 0.05493164063 + 0.46875r + r2 = 0.07055664063 Factor a perfect square on the left side: (r + 0.234375)(r + 0.234375) = 0.07055664063 Calculate the square root of the right side: 0.265625 Break this problem into two subproblems by setting (r + 0.234375) equal to 0.265625 and -0.265625.Subproblem 1
r + 0.234375 = 0.265625 Simplifying r + 0.234375 = 0.265625 Reorder the terms: 0.234375 + r = 0.265625 Solving 0.234375 + r = 0.265625 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.234375' to each side of the equation. 0.234375 + -0.234375 + r = 0.265625 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + r = 0.265625 + -0.234375 r = 0.265625 + -0.234375 Combine like terms: 0.265625 + -0.234375 = 0.03125 r = 0.03125 Simplifying r = 0.03125Subproblem 2
r + 0.234375 = -0.265625 Simplifying r + 0.234375 = -0.265625 Reorder the terms: 0.234375 + r = -0.265625 Solving 0.234375 + r = -0.265625 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.234375' to each side of the equation. 0.234375 + -0.234375 + r = -0.265625 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + r = -0.265625 + -0.234375 r = -0.265625 + -0.234375 Combine like terms: -0.265625 + -0.234375 = -0.5 r = -0.5 Simplifying r = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.03125, -0.5}
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