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Simplifying r2 = 14r + 26 Reorder the terms: r2 = 26 + 14r Solving r2 = 26 + 14r Solving for variable 'r'. Reorder the terms: -26 + -14r + r2 = 26 + 14r + -26 + -14r Reorder the terms: -26 + -14r + r2 = 26 + -26 + 14r + -14r Combine like terms: 26 + -26 = 0 -26 + -14r + r2 = 0 + 14r + -14r -26 + -14r + r2 = 14r + -14r Combine like terms: 14r + -14r = 0 -26 + -14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -14r + 26 + r2 = 0 + 26 Reorder the terms: -26 + 26 + -14r + r2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -14r + r2 = 0 + 26 -14r + r2 = 0 + 26 Combine like terms: 0 + 26 = 26 -14r + r2 = 26 The r term is -14r. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14r + 49 + r2 = 26 + 49 Reorder the terms: 49 + -14r + r2 = 26 + 49 Combine like terms: 26 + 49 = 75 49 + -14r + r2 = 75 Factor a perfect square on the left side: (r + -7)(r + -7) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (r + -7) equal to 8.660254038 and -8.660254038.Subproblem 1
r + -7 = 8.660254038 Simplifying r + -7 = 8.660254038 Reorder the terms: -7 + r = 8.660254038 Solving -7 + r = 8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = 8.660254038 + 7 Combine like terms: -7 + 7 = 0 0 + r = 8.660254038 + 7 r = 8.660254038 + 7 Combine like terms: 8.660254038 + 7 = 15.660254038 r = 15.660254038 Simplifying r = 15.660254038Subproblem 2
r + -7 = -8.660254038 Simplifying r + -7 = -8.660254038 Reorder the terms: -7 + r = -8.660254038 Solving -7 + r = -8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = -8.660254038 + 7 Combine like terms: -7 + 7 = 0 0 + r = -8.660254038 + 7 r = -8.660254038 + 7 Combine like terms: -8.660254038 + 7 = -1.660254038 r = -1.660254038 Simplifying r = -1.660254038Solution
The solution to the problem is based on the solutions from the subproblems. r = {15.660254038, -1.660254038}
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