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Simplifying 2r2 + 15r + -28 = 0 Reorder the terms: -28 + 15r + 2r2 = 0 Solving -28 + 15r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 7.5r + r2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 7.5r + 14 + r2 = 0 + 14 Reorder the terms: -14 + 14 + 7.5r + r2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 7.5r + r2 = 0 + 14 7.5r + r2 = 0 + 14 Combine like terms: 0 + 14 = 14 7.5r + r2 = 14 The r term is 7.5r. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5r + 14.0625 + r2 = 14 + 14.0625 Reorder the terms: 14.0625 + 7.5r + r2 = 14 + 14.0625 Combine like terms: 14 + 14.0625 = 28.0625 14.0625 + 7.5r + r2 = 28.0625 Factor a perfect square on the left side: (r + 3.75)(r + 3.75) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (r + 3.75) equal to 5.297405025 and -5.297405025.Subproblem 1
r + 3.75 = 5.297405025 Simplifying r + 3.75 = 5.297405025 Reorder the terms: 3.75 + r = 5.297405025 Solving 3.75 + r = 5.297405025 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + r = 5.297405025 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + r = 5.297405025 + -3.75 r = 5.297405025 + -3.75 Combine like terms: 5.297405025 + -3.75 = 1.547405025 r = 1.547405025 Simplifying r = 1.547405025Subproblem 2
r + 3.75 = -5.297405025 Simplifying r + 3.75 = -5.297405025 Reorder the terms: 3.75 + r = -5.297405025 Solving 3.75 + r = -5.297405025 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + r = -5.297405025 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + r = -5.297405025 + -3.75 r = -5.297405025 + -3.75 Combine like terms: -5.297405025 + -3.75 = -9.047405025 r = -9.047405025 Simplifying r = -9.047405025Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.547405025, -9.047405025}
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