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Simplifying 3r2 + -5r + -27 = 0 Reorder the terms: -27 + -5r + 3r2 = 0 Solving -27 + -5r + 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'. -9 + -1.666666667r + r2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1.666666667r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + -1.666666667r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1.666666667r + r2 = 0 + 9 -1.666666667r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1.666666667r + r2 = 9 The r term is -1.666666667r. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667r + 0.6944444447 + r2 = 9 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667r + r2 = 9 + 0.6944444447 Combine like terms: 9 + 0.6944444447 = 9.6944444447 0.6944444447 + -1.666666667r + r2 = 9.6944444447 Factor a perfect square on the left side: (r + -0.8333333335)(r + -0.8333333335) = 9.6944444447 Calculate the square root of the right side: 3.113590282 Break this problem into two subproblems by setting (r + -0.8333333335) equal to 3.113590282 and -3.113590282.Subproblem 1
r + -0.8333333335 = 3.113590282 Simplifying r + -0.8333333335 = 3.113590282 Reorder the terms: -0.8333333335 + r = 3.113590282 Solving -0.8333333335 + r = 3.113590282 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + r = 3.113590282 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + r = 3.113590282 + 0.8333333335 r = 3.113590282 + 0.8333333335 Combine like terms: 3.113590282 + 0.8333333335 = 3.9469236155 r = 3.9469236155 Simplifying r = 3.9469236155Subproblem 2
r + -0.8333333335 = -3.113590282 Simplifying r + -0.8333333335 = -3.113590282 Reorder the terms: -0.8333333335 + r = -3.113590282 Solving -0.8333333335 + r = -3.113590282 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + r = -3.113590282 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + r = -3.113590282 + 0.8333333335 r = -3.113590282 + 0.8333333335 Combine like terms: -3.113590282 + 0.8333333335 = -2.2802569485 r = -2.2802569485 Simplifying r = -2.2802569485Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.9469236155, -2.2802569485}
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