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Simplifying 250r2 + 500r + -41.6 = 0 Reorder the terms: -41.6 + 500r + 250r2 = 0 Solving -41.6 + 500r + 250r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 250 the coefficient of the squared term: Divide each side by '250'. -0.1664 + 2r + r2 = 0 Move the constant term to the right: Add '0.1664' to each side of the equation. -0.1664 + 2r + 0.1664 + r2 = 0 + 0.1664 Reorder the terms: -0.1664 + 0.1664 + 2r + r2 = 0 + 0.1664 Combine like terms: -0.1664 + 0.1664 = 0.0000 0.0000 + 2r + r2 = 0 + 0.1664 2r + r2 = 0 + 0.1664 Combine like terms: 0 + 0.1664 = 0.1664 2r + r2 = 0.1664 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 0.1664 + 1 Reorder the terms: 1 + 2r + r2 = 0.1664 + 1 Combine like terms: 0.1664 + 1 = 1.1664 1 + 2r + r2 = 1.1664 Factor a perfect square on the left side: (r + 1)(r + 1) = 1.1664 Calculate the square root of the right side: 1.08 Break this problem into two subproblems by setting (r + 1) equal to 1.08 and -1.08.Subproblem 1
r + 1 = 1.08 Simplifying r + 1 = 1.08 Reorder the terms: 1 + r = 1.08 Solving 1 + r = 1.08 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 1.08 + -1 Combine like terms: 1 + -1 = 0 0 + r = 1.08 + -1 r = 1.08 + -1 Combine like terms: 1.08 + -1 = 0.08 r = 0.08 Simplifying r = 0.08Subproblem 2
r + 1 = -1.08 Simplifying r + 1 = -1.08 Reorder the terms: 1 + r = -1.08 Solving 1 + r = -1.08 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -1.08 + -1 Combine like terms: 1 + -1 = 0 0 + r = -1.08 + -1 r = -1.08 + -1 Combine like terms: -1.08 + -1 = -2.08 r = -2.08 Simplifying r = -2.08Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.08, -2.08}
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