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Simplifying r2 = 35 + -5r Solving r2 = 35 + -5r Solving for variable 'r'. Reorder the terms: -35 + 5r + r2 = 35 + -5r + -35 + 5r Reorder the terms: -35 + 5r + r2 = 35 + -35 + -5r + 5r Combine like terms: 35 + -35 = 0 -35 + 5r + r2 = 0 + -5r + 5r -35 + 5r + r2 = -5r + 5r Combine like terms: -5r + 5r = 0 -35 + 5r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 5r + 35 + r2 = 0 + 35 Reorder the terms: -35 + 35 + 5r + r2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 5r + r2 = 0 + 35 5r + r2 = 0 + 35 Combine like terms: 0 + 35 = 35 5r + r2 = 35 The r term is 5r. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5r + 6.25 + r2 = 35 + 6.25 Reorder the terms: 6.25 + 5r + r2 = 35 + 6.25 Combine like terms: 35 + 6.25 = 41.25 6.25 + 5r + r2 = 41.25 Factor a perfect square on the left side: (r + 2.5)(r + 2.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (r + 2.5) equal to 6.422616289 and -6.422616289.Subproblem 1
r + 2.5 = 6.422616289 Simplifying r + 2.5 = 6.422616289 Reorder the terms: 2.5 + r = 6.422616289 Solving 2.5 + r = 6.422616289 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 6.422616289 + -2.5 r = 6.422616289 + -2.5 Combine like terms: 6.422616289 + -2.5 = 3.922616289 r = 3.922616289 Simplifying r = 3.922616289Subproblem 2
r + 2.5 = -6.422616289 Simplifying r + 2.5 = -6.422616289 Reorder the terms: 2.5 + r = -6.422616289 Solving 2.5 + r = -6.422616289 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -6.422616289 + -2.5 r = -6.422616289 + -2.5 Combine like terms: -6.422616289 + -2.5 = -8.922616289 r = -8.922616289 Simplifying r = -8.922616289Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.922616289, -8.922616289}
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