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Simplifying r(r + -0.18) = 0.0294 Reorder the terms: r(-0.18 + r) = 0.0294 (-0.18 * r + r * r) = 0.0294 (-0.18r + r2) = 0.0294 Solving -0.18r + r2 = 0.0294 Solving for variable 'r'. Reorder the terms: -0.0294 + -0.18r + r2 = 0.0294 + -0.0294 Combine like terms: 0.0294 + -0.0294 = 0.0000 -0.0294 + -0.18r + r2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '0.0294' to each side of the equation. -0.0294 + -0.18r + 0.0294 + r2 = 0.0000 + 0.0294 Reorder the terms: -0.0294 + 0.0294 + -0.18r + r2 = 0.0000 + 0.0294 Combine like terms: -0.0294 + 0.0294 = 0.0000 0.0000 + -0.18r + r2 = 0.0000 + 0.0294 -0.18r + r2 = 0.0000 + 0.0294 Combine like terms: 0.0000 + 0.0294 = 0.0294 -0.18r + r2 = 0.0294 The r term is -0.18r. Take half its coefficient (-0.09). Square it (0.0081) and add it to both sides. Add '0.0081' to each side of the equation. -0.18r + 0.0081 + r2 = 0.0294 + 0.0081 Reorder the terms: 0.0081 + -0.18r + r2 = 0.0294 + 0.0081 Combine like terms: 0.0294 + 0.0081 = 0.0375 0.0081 + -0.18r + r2 = 0.0375 Factor a perfect square on the left side: (r + -0.09)(r + -0.09) = 0.0375 Calculate the square root of the right side: 0.193649167 Break this problem into two subproblems by setting (r + -0.09) equal to 0.193649167 and -0.193649167.Subproblem 1
r + -0.09 = 0.193649167 Simplifying r + -0.09 = 0.193649167 Reorder the terms: -0.09 + r = 0.193649167 Solving -0.09 + r = 0.193649167 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.09' to each side of the equation. -0.09 + 0.09 + r = 0.193649167 + 0.09 Combine like terms: -0.09 + 0.09 = 0.00 0.00 + r = 0.193649167 + 0.09 r = 0.193649167 + 0.09 Combine like terms: 0.193649167 + 0.09 = 0.283649167 r = 0.283649167 Simplifying r = 0.283649167Subproblem 2
r + -0.09 = -0.193649167 Simplifying r + -0.09 = -0.193649167 Reorder the terms: -0.09 + r = -0.193649167 Solving -0.09 + r = -0.193649167 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.09' to each side of the equation. -0.09 + 0.09 + r = -0.193649167 + 0.09 Combine like terms: -0.09 + 0.09 = 0.00 0.00 + r = -0.193649167 + 0.09 r = -0.193649167 + 0.09 Combine like terms: -0.193649167 + 0.09 = -0.103649167 r = -0.103649167 Simplifying r = -0.103649167Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.283649167, -0.103649167}
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