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Simplifying 3r2 + 46r + -120 = 0 Reorder the terms: -120 + 46r + 3r2 = 0 Solving -120 + 46r + 3r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -40 + 15.33333333r + r2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 15.33333333r + 40 + r2 = 0 + 40 Reorder the terms: -40 + 40 + 15.33333333r + r2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 15.33333333r + r2 = 0 + 40 15.33333333r + r2 = 0 + 40 Combine like terms: 0 + 40 = 40 15.33333333r + r2 = 40 The r term is 15.33333333r. Take half its coefficient (7.666666665). Square it (58.77777775) and add it to both sides. Add '58.77777775' to each side of the equation. 15.33333333r + 58.77777775 + r2 = 40 + 58.77777775 Reorder the terms: 58.77777775 + 15.33333333r + r2 = 40 + 58.77777775 Combine like terms: 40 + 58.77777775 = 98.77777775 58.77777775 + 15.33333333r + r2 = 98.77777775 Factor a perfect square on the left side: (r + 7.666666665)(r + 7.666666665) = 98.77777775 Calculate the square root of the right side: 9.938701009 Break this problem into two subproblems by setting (r + 7.666666665) equal to 9.938701009 and -9.938701009.Subproblem 1
r + 7.666666665 = 9.938701009 Simplifying r + 7.666666665 = 9.938701009 Reorder the terms: 7.666666665 + r = 9.938701009 Solving 7.666666665 + r = 9.938701009 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.666666665' to each side of the equation. 7.666666665 + -7.666666665 + r = 9.938701009 + -7.666666665 Combine like terms: 7.666666665 + -7.666666665 = 0.000000000 0.000000000 + r = 9.938701009 + -7.666666665 r = 9.938701009 + -7.666666665 Combine like terms: 9.938701009 + -7.666666665 = 2.272034344 r = 2.272034344 Simplifying r = 2.272034344Subproblem 2
r + 7.666666665 = -9.938701009 Simplifying r + 7.666666665 = -9.938701009 Reorder the terms: 7.666666665 + r = -9.938701009 Solving 7.666666665 + r = -9.938701009 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.666666665' to each side of the equation. 7.666666665 + -7.666666665 + r = -9.938701009 + -7.666666665 Combine like terms: 7.666666665 + -7.666666665 = 0.000000000 0.000000000 + r = -9.938701009 + -7.666666665 r = -9.938701009 + -7.666666665 Combine like terms: -9.938701009 + -7.666666665 = -17.605367674 r = -17.605367674 Simplifying r = -17.605367674Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.272034344, -17.605367674}
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