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Simplifying r2 + -22r = -31 Reorder the terms: -22r + r2 = -31 Solving -22r + r2 = -31 Solving for variable 'r'. Reorder the terms: 31 + -22r + r2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -22r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -22r + -31 + r2 = 0 + -31 Reorder the terms: 31 + -31 + -22r + r2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -22r + r2 = 0 + -31 -22r + r2 = 0 + -31 Combine like terms: 0 + -31 = -31 -22r + r2 = -31 The r term is -22r. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22r + 121 + r2 = -31 + 121 Reorder the terms: 121 + -22r + r2 = -31 + 121 Combine like terms: -31 + 121 = 90 121 + -22r + r2 = 90 Factor a perfect square on the left side: (r + -11)(r + -11) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (r + -11) equal to 9.486832981 and -9.486832981.Subproblem 1
r + -11 = 9.486832981 Simplifying r + -11 = 9.486832981 Reorder the terms: -11 + r = 9.486832981 Solving -11 + r = 9.486832981 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + r = 9.486832981 + 11 Combine like terms: -11 + 11 = 0 0 + r = 9.486832981 + 11 r = 9.486832981 + 11 Combine like terms: 9.486832981 + 11 = 20.486832981 r = 20.486832981 Simplifying r = 20.486832981Subproblem 2
r + -11 = -9.486832981 Simplifying r + -11 = -9.486832981 Reorder the terms: -11 + r = -9.486832981 Solving -11 + r = -9.486832981 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + r = -9.486832981 + 11 Combine like terms: -11 + 11 = 0 0 + r = -9.486832981 + 11 r = -9.486832981 + 11 Combine like terms: -9.486832981 + 11 = 1.513167019 r = 1.513167019 Simplifying r = 1.513167019Solution
The solution to the problem is based on the solutions from the subproblems. r = {20.486832981, 1.513167019}
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