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Simplifying r2 + 12r + -18 = 0 Reorder the terms: -18 + 12r + r2 = 0 Solving -18 + 12r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 12r + 18 + r2 = 0 + 18 Reorder the terms: -18 + 18 + 12r + r2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 12r + r2 = 0 + 18 12r + r2 = 0 + 18 Combine like terms: 0 + 18 = 18 12r + r2 = 18 The r term is 12r. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12r + 36 + r2 = 18 + 36 Reorder the terms: 36 + 12r + r2 = 18 + 36 Combine like terms: 18 + 36 = 54 36 + 12r + r2 = 54 Factor a perfect square on the left side: (r + 6)(r + 6) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (r + 6) equal to 7.348469228 and -7.348469228.Subproblem 1
r + 6 = 7.348469228 Simplifying r + 6 = 7.348469228 Reorder the terms: 6 + r = 7.348469228 Solving 6 + r = 7.348469228 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + r = 7.348469228 + -6 r = 7.348469228 + -6 Combine like terms: 7.348469228 + -6 = 1.348469228 r = 1.348469228 Simplifying r = 1.348469228Subproblem 2
r + 6 = -7.348469228 Simplifying r + 6 = -7.348469228 Reorder the terms: 6 + r = -7.348469228 Solving 6 + r = -7.348469228 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + r = -7.348469228 + -6 r = -7.348469228 + -6 Combine like terms: -7.348469228 + -6 = -13.348469228 r = -13.348469228 Simplifying r = -13.348469228Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.348469228, -13.348469228}
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