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Simplifying 12r2 + -13r + 2 = 0 Reorder the terms: 2 + -13r + 12r2 = 0 Solving 2 + -13r + 12r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + -1.083333333r + r2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1.083333333r + -0.1666666667 + r2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1.083333333r + r2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1.083333333r + r2 = 0 + -0.1666666667 -1.083333333r + r2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1.083333333r + r2 = -0.1666666667 The r term is -1.083333333r. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333r + 0.2934027776 + r2 = -0.1666666667 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333r + r2 = -0.1666666667 + 0.2934027776 Combine like terms: -0.1666666667 + 0.2934027776 = 0.1267361109 0.2934027776 + -1.083333333r + r2 = 0.1267361109 Factor a perfect square on the left side: (r + -0.5416666665)(r + -0.5416666665) = 0.1267361109 Calculate the square root of the right side: 0.356000156 Break this problem into two subproblems by setting (r + -0.5416666665) equal to 0.356000156 and -0.356000156.Subproblem 1
r + -0.5416666665 = 0.356000156 Simplifying r + -0.5416666665 = 0.356000156 Reorder the terms: -0.5416666665 + r = 0.356000156 Solving -0.5416666665 + r = 0.356000156 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + r = 0.356000156 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + r = 0.356000156 + 0.5416666665 r = 0.356000156 + 0.5416666665 Combine like terms: 0.356000156 + 0.5416666665 = 0.8976668225 r = 0.8976668225 Simplifying r = 0.8976668225Subproblem 2
r + -0.5416666665 = -0.356000156 Simplifying r + -0.5416666665 = -0.356000156 Reorder the terms: -0.5416666665 + r = -0.356000156 Solving -0.5416666665 + r = -0.356000156 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + r = -0.356000156 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + r = -0.356000156 + 0.5416666665 r = -0.356000156 + 0.5416666665 Combine like terms: -0.356000156 + 0.5416666665 = 0.1856665105 r = 0.1856665105 Simplifying r = 0.1856665105Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.8976668225, 0.1856665105}
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