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Simplifying 9r2 + -10r + -81 = 0 Reorder the terms: -81 + -10r + 9r2 = 0 Solving -81 + -10r + 9r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -9 + -1.111111111r + r2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1.111111111r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + -1.111111111r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1.111111111r + r2 = 0 + 9 -1.111111111r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1.111111111r + r2 = 9 The r term is -1.111111111r. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111r + 0.3086419752 + r2 = 9 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111r + r2 = 9 + 0.3086419752 Combine like terms: 9 + 0.3086419752 = 9.3086419752 0.3086419752 + -1.111111111r + r2 = 9.3086419752 Factor a perfect square on the left side: (r + -0.5555555555)(r + -0.5555555555) = 9.3086419752 Calculate the square root of the right side: 3.051006715 Break this problem into two subproblems by setting (r + -0.5555555555) equal to 3.051006715 and -3.051006715.Subproblem 1
r + -0.5555555555 = 3.051006715 Simplifying r + -0.5555555555 = 3.051006715 Reorder the terms: -0.5555555555 + r = 3.051006715 Solving -0.5555555555 + r = 3.051006715 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + r = 3.051006715 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + r = 3.051006715 + 0.5555555555 r = 3.051006715 + 0.5555555555 Combine like terms: 3.051006715 + 0.5555555555 = 3.6065622705 r = 3.6065622705 Simplifying r = 3.6065622705Subproblem 2
r + -0.5555555555 = -3.051006715 Simplifying r + -0.5555555555 = -3.051006715 Reorder the terms: -0.5555555555 + r = -3.051006715 Solving -0.5555555555 + r = -3.051006715 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + r = -3.051006715 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + r = -3.051006715 + 0.5555555555 r = -3.051006715 + 0.5555555555 Combine like terms: -3.051006715 + 0.5555555555 = -2.4954511595 r = -2.4954511595 Simplifying r = -2.4954511595Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.6065622705, -2.4954511595}
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