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Simplifying 22r2 + -43r + -44 = 0 Reorder the terms: -44 + -43r + 22r2 = 0 Solving -44 + -43r + 22r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -2 + -1.954545455r + r2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.954545455r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + -1.954545455r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.954545455r + r2 = 0 + 2 -1.954545455r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.954545455r + r2 = 2 The r term is -1.954545455r. Take half its coefficient (-0.9772727275). Square it (0.9550619839) and add it to both sides. Add '0.9550619839' to each side of the equation. -1.954545455r + 0.9550619839 + r2 = 2 + 0.9550619839 Reorder the terms: 0.9550619839 + -1.954545455r + r2 = 2 + 0.9550619839 Combine like terms: 2 + 0.9550619839 = 2.9550619839 0.9550619839 + -1.954545455r + r2 = 2.9550619839 Factor a perfect square on the left side: (r + -0.9772727275)(r + -0.9772727275) = 2.9550619839 Calculate the square root of the right side: 1.719029373 Break this problem into two subproblems by setting (r + -0.9772727275) equal to 1.719029373 and -1.719029373.Subproblem 1
r + -0.9772727275 = 1.719029373 Simplifying r + -0.9772727275 = 1.719029373 Reorder the terms: -0.9772727275 + r = 1.719029373 Solving -0.9772727275 + r = 1.719029373 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.9772727275' to each side of the equation. -0.9772727275 + 0.9772727275 + r = 1.719029373 + 0.9772727275 Combine like terms: -0.9772727275 + 0.9772727275 = 0.0000000000 0.0000000000 + r = 1.719029373 + 0.9772727275 r = 1.719029373 + 0.9772727275 Combine like terms: 1.719029373 + 0.9772727275 = 2.6963021005 r = 2.6963021005 Simplifying r = 2.6963021005Subproblem 2
r + -0.9772727275 = -1.719029373 Simplifying r + -0.9772727275 = -1.719029373 Reorder the terms: -0.9772727275 + r = -1.719029373 Solving -0.9772727275 + r = -1.719029373 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.9772727275' to each side of the equation. -0.9772727275 + 0.9772727275 + r = -1.719029373 + 0.9772727275 Combine like terms: -0.9772727275 + 0.9772727275 = 0.0000000000 0.0000000000 + r = -1.719029373 + 0.9772727275 r = -1.719029373 + 0.9772727275 Combine like terms: -1.719029373 + 0.9772727275 = -0.7417566455 r = -0.7417566455 Simplifying r = -0.7417566455Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.6963021005, -0.7417566455}
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