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Simplifying r2 + -9r + -38 = 0 Reorder the terms: -38 + -9r + r2 = 0 Solving -38 + -9r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -9r + 38 + r2 = 0 + 38 Reorder the terms: -38 + 38 + -9r + r2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -9r + r2 = 0 + 38 -9r + r2 = 0 + 38 Combine like terms: 0 + 38 = 38 -9r + r2 = 38 The r term is -9r. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9r + 20.25 + r2 = 38 + 20.25 Reorder the terms: 20.25 + -9r + r2 = 38 + 20.25 Combine like terms: 38 + 20.25 = 58.25 20.25 + -9r + r2 = 58.25 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (r + -4.5) equal to 7.632168761 and -7.632168761.Subproblem 1
r + -4.5 = 7.632168761 Simplifying r + -4.5 = 7.632168761 Reorder the terms: -4.5 + r = 7.632168761 Solving -4.5 + r = 7.632168761 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = 7.632168761 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 7.632168761 + 4.5 r = 7.632168761 + 4.5 Combine like terms: 7.632168761 + 4.5 = 12.132168761 r = 12.132168761 Simplifying r = 12.132168761Subproblem 2
r + -4.5 = -7.632168761 Simplifying r + -4.5 = -7.632168761 Reorder the terms: -4.5 + r = -7.632168761 Solving -4.5 + r = -7.632168761 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = -7.632168761 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -7.632168761 + 4.5 r = -7.632168761 + 4.5 Combine like terms: -7.632168761 + 4.5 = -3.132168761 r = -3.132168761 Simplifying r = -3.132168761Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.132168761, -3.132168761}
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