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Simplifying 9r2 + -17 = r Reorder the terms: -17 + 9r2 = r Solving -17 + 9r2 = r Solving for variable 'r'. Reorder the terms: -17 + -1r + 9r2 = r + -1r Combine like terms: r + -1r = 0 -17 + -1r + 9r2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + -0.1111111111r + r2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + -0.1111111111r + 1.888888889 + r2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + -0.1111111111r + r2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + -0.1111111111r + r2 = 0 + 1.888888889 -0.1111111111r + r2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 -0.1111111111r + r2 = 1.888888889 The r term is -0.1111111111r. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111r + 0.003086419752 + r2 = 1.888888889 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111r + r2 = 1.888888889 + 0.003086419752 Combine like terms: 1.888888889 + 0.003086419752 = 1.891975308752 0.003086419752 + -0.1111111111r + r2 = 1.891975308752 Factor a perfect square on the left side: (r + -0.05555555555)(r + -0.05555555555) = 1.891975308752 Calculate the square root of the right side: 1.375490934 Break this problem into two subproblems by setting (r + -0.05555555555) equal to 1.375490934 and -1.375490934.Subproblem 1
r + -0.05555555555 = 1.375490934 Simplifying r + -0.05555555555 = 1.375490934 Reorder the terms: -0.05555555555 + r = 1.375490934 Solving -0.05555555555 + r = 1.375490934 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + r = 1.375490934 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + r = 1.375490934 + 0.05555555555 r = 1.375490934 + 0.05555555555 Combine like terms: 1.375490934 + 0.05555555555 = 1.43104648955 r = 1.43104648955 Simplifying r = 1.43104648955Subproblem 2
r + -0.05555555555 = -1.375490934 Simplifying r + -0.05555555555 = -1.375490934 Reorder the terms: -0.05555555555 + r = -1.375490934 Solving -0.05555555555 + r = -1.375490934 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + r = -1.375490934 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + r = -1.375490934 + 0.05555555555 r = -1.375490934 + 0.05555555555 Combine like terms: -1.375490934 + 0.05555555555 = -1.31993537845 r = -1.31993537845 Simplifying r = -1.31993537845Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.43104648955, -1.31993537845}
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