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Simplifying 2r2 + 7r + -33 = 0 Reorder the terms: -33 + 7r + 2r2 = 0 Solving -33 + 7r + 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'. -16.5 + 3.5r + r2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 3.5r + 16.5 + r2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 3.5r + r2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 3.5r + r2 = 0 + 16.5 3.5r + r2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 3.5r + r2 = 16.5 The r term is 3.5r. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5r + 3.0625 + r2 = 16.5 + 3.0625 Reorder the terms: 3.0625 + 3.5r + r2 = 16.5 + 3.0625 Combine like terms: 16.5 + 3.0625 = 19.5625 3.0625 + 3.5r + r2 = 19.5625 Factor a perfect square on the left side: (r + 1.75)(r + 1.75) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (r + 1.75) equal to 4.422951503 and -4.422951503.Subproblem 1
r + 1.75 = 4.422951503 Simplifying r + 1.75 = 4.422951503 Reorder the terms: 1.75 + r = 4.422951503 Solving 1.75 + r = 4.422951503 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + r = 4.422951503 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + r = 4.422951503 + -1.75 r = 4.422951503 + -1.75 Combine like terms: 4.422951503 + -1.75 = 2.672951503 r = 2.672951503 Simplifying r = 2.672951503Subproblem 2
r + 1.75 = -4.422951503 Simplifying r + 1.75 = -4.422951503 Reorder the terms: 1.75 + r = -4.422951503 Solving 1.75 + r = -4.422951503 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + r = -4.422951503 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + r = -4.422951503 + -1.75 r = -4.422951503 + -1.75 Combine like terms: -4.422951503 + -1.75 = -6.172951503 r = -6.172951503 Simplifying r = -6.172951503Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.672951503, -6.172951503}
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