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Simplifying r2 + -12r = 27 Reorder the terms: -12r + r2 = 27 Solving -12r + r2 = 27 Solving for variable 'r'. Reorder the terms: -27 + -12r + r2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -12r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -12r + 27 + r2 = 0 + 27 Reorder the terms: -27 + 27 + -12r + r2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -12r + r2 = 0 + 27 -12r + r2 = 0 + 27 Combine like terms: 0 + 27 = 27 -12r + r2 = 27 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 = 27 + 36 Reorder the terms: 36 + -12r + r2 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + -12r + r2 = 63 Factor a perfect square on the left side: (r + -6)(r + -6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (r + -6) equal to 7.937253933 and -7.937253933.Subproblem 1
r + -6 = 7.937253933 Simplifying r + -6 = 7.937253933 Reorder the terms: -6 + r = 7.937253933 Solving -6 + r = 7.937253933 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 = 7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + r = 7.937253933 + 6 r = 7.937253933 + 6 Combine like terms: 7.937253933 + 6 = 13.937253933 r = 13.937253933 Simplifying r = 13.937253933Subproblem 2
r + -6 = -7.937253933 Simplifying r + -6 = -7.937253933 Reorder the terms: -6 + r = -7.937253933 Solving -6 + r = -7.937253933 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 = -7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + r = -7.937253933 + 6 r = -7.937253933 + 6 Combine like terms: -7.937253933 + 6 = -1.937253933 r = -1.937253933 Simplifying r = -1.937253933Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.937253933, -1.937253933}
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