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Simplifying r2 + 26r + 47 = 0 Reorder the terms: 47 + 26r + r2 = 0 Solving 47 + 26r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 26r + -47 + r2 = 0 + -47 Reorder the terms: 47 + -47 + 26r + r2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 26r + r2 = 0 + -47 26r + r2 = 0 + -47 Combine like terms: 0 + -47 = -47 26r + r2 = -47 The r term is 26r. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26r + 169 + r2 = -47 + 169 Reorder the terms: 169 + 26r + r2 = -47 + 169 Combine like terms: -47 + 169 = 122 169 + 26r + r2 = 122 Factor a perfect square on the left side: (r + 13)(r + 13) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (r + 13) equal to 11.045361017 and -11.045361017.Subproblem 1
r + 13 = 11.045361017 Simplifying r + 13 = 11.045361017 Reorder the terms: 13 + r = 11.045361017 Solving 13 + r = 11.045361017 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + r = 11.045361017 + -13 Combine like terms: 13 + -13 = 0 0 + r = 11.045361017 + -13 r = 11.045361017 + -13 Combine like terms: 11.045361017 + -13 = -1.954638983 r = -1.954638983 Simplifying r = -1.954638983Subproblem 2
r + 13 = -11.045361017 Simplifying r + 13 = -11.045361017 Reorder the terms: 13 + r = -11.045361017 Solving 13 + r = -11.045361017 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + r = -11.045361017 + -13 Combine like terms: 13 + -13 = 0 0 + r = -11.045361017 + -13 r = -11.045361017 + -13 Combine like terms: -11.045361017 + -13 = -24.045361017 r = -24.045361017 Simplifying r = -24.045361017Solution
The solution to the problem is based on the solutions from the subproblems. r = {-1.954638983, -24.045361017}
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