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Simplifying r2 + 12r + -6 = 0 Reorder the terms: -6 + 12r + r2 = 0 Solving -6 + 12r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 12r + 6 + r2 = 0 + 6 Reorder the terms: -6 + 6 + 12r + r2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 12r + r2 = 0 + 6 12r + r2 = 0 + 6 Combine like terms: 0 + 6 = 6 12r + r2 = 6 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 = 6 + 36 Reorder the terms: 36 + 12r + r2 = 6 + 36 Combine like terms: 6 + 36 = 42 36 + 12r + r2 = 42 Factor a perfect square on the left side: (r + 6)(r + 6) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (r + 6) equal to 6.480740698 and -6.480740698.Subproblem 1
r + 6 = 6.480740698 Simplifying r + 6 = 6.480740698 Reorder the terms: 6 + r = 6.480740698 Solving 6 + r = 6.480740698 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 = 6.480740698 + -6 Combine like terms: 6 + -6 = 0 0 + r = 6.480740698 + -6 r = 6.480740698 + -6 Combine like terms: 6.480740698 + -6 = 0.480740698 r = 0.480740698 Simplifying r = 0.480740698Subproblem 2
r + 6 = -6.480740698 Simplifying r + 6 = -6.480740698 Reorder the terms: 6 + r = -6.480740698 Solving 6 + r = -6.480740698 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 = -6.480740698 + -6 Combine like terms: 6 + -6 = 0 0 + r = -6.480740698 + -6 r = -6.480740698 + -6 Combine like terms: -6.480740698 + -6 = -12.480740698 r = -12.480740698 Simplifying r = -12.480740698Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.480740698, -12.480740698}
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