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Simplifying r2 + 14r = 37 Reorder the terms: 14r + r2 = 37 Solving 14r + r2 = 37 Solving for variable 'r'. Reorder the terms: -37 + 14r + r2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 14r + 37 + r2 = 0 + 37 Reorder the terms: -37 + 37 + 14r + r2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 14r + r2 = 0 + 37 14r + r2 = 0 + 37 Combine like terms: 0 + 37 = 37 14r + r2 = 37 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 = 37 + 49 Reorder the terms: 49 + 14r + r2 = 37 + 49 Combine like terms: 37 + 49 = 86 49 + 14r + r2 = 86 Factor a perfect square on the left side: (r + 7)(r + 7) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (r + 7) equal to 9.273618495 and -9.273618495.Subproblem 1
r + 7 = 9.273618495 Simplifying r + 7 = 9.273618495 Reorder the terms: 7 + r = 9.273618495 Solving 7 + r = 9.273618495 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 = 9.273618495 + -7 Combine like terms: 7 + -7 = 0 0 + r = 9.273618495 + -7 r = 9.273618495 + -7 Combine like terms: 9.273618495 + -7 = 2.273618495 r = 2.273618495 Simplifying r = 2.273618495Subproblem 2
r + 7 = -9.273618495 Simplifying r + 7 = -9.273618495 Reorder the terms: 7 + r = -9.273618495 Solving 7 + r = -9.273618495 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 = -9.273618495 + -7 Combine like terms: 7 + -7 = 0 0 + r = -9.273618495 + -7 r = -9.273618495 + -7 Combine like terms: -9.273618495 + -7 = -16.273618495 r = -16.273618495 Simplifying r = -16.273618495Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.273618495, -16.273618495}
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